Q. If a circle is centered at (0, 0) with a radius of 5, which of the following points lies outside the circle?
-
A.
(3, 4)
-
B.
(0, 5)
-
C.
(5, 0)
-
D.
(6, 0)
Solution
The equation of the circle is x² + y² = 25. The point (6, 0) gives 6² + 0² = 36, which is greater than 25, hence it lies outside.
Correct Answer:
D
— (6, 0)
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Q. If a line has the equation 2x - 3y + 6 = 0, what is the y-intercept of the line?
Solution
To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, thus y = 2.
Correct Answer:
B
— 2
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Q. If a line has the equation 3x - 4y + 12 = 0, what is its y-intercept?
Solution
To find the y-intercept, set x = 0. The equation becomes -4y + 12 = 0, leading to y = 3.
Correct Answer:
A
— 3
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Q. If a line has the equation 3x - 4y = 12, what is the y-intercept of the line?
Solution
To find the y-intercept, set x = 0. The equation becomes -4y = 12, thus y = -3. The y-intercept is (0, -3).
Correct Answer:
A
— 3
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Q. If a line passes through the points (1, 2) and (3, 6), what is the slope of the line?
Solution
The slope m is calculated as (6-2)/(3-1) = 4/2 = 2.
Correct Answer:
A
— 2
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Q. If the coordinates of a point are (x, y) such that x + y = 10 and x - y = 2, what are the coordinates of the point?
-
A.
(6, 4)
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B.
(5, 5)
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C.
(4, 6)
-
D.
(2, 8)
Solution
Solving the equations x + y = 10 and x - y = 2 simultaneously gives x = 6 and y = 4.
Correct Answer:
A
— (6, 4)
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Q. If the coordinates of point C are (x, 0) and it lies on the line y = -3x + 6, what is the value of x?
Solution
Setting y = 0 in the equation -3x + 6 = 0 gives x = 2.
Correct Answer:
B
— 2
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Q. If the coordinates of points D and E are (2, 3) and (4, 7) respectively, what is the slope of the line DE?
Solution
The slope m is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4/2 = 2.
Correct Answer:
B
— 2
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Q. If the equation of a line is given as 2x - 3y + 6 = 0, what is the y-intercept of the line?
Solution
To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, leading to y = 2.
Correct Answer:
B
— 2
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Q. If the equation of a line is given as 3x - 4y + 12 = 0, what is the y-intercept of the line?
Solution
To find the y-intercept, set x = 0. The equation becomes -4y + 12 = 0, leading to y = 3.
Correct Answer:
A
— 3
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Q. If the equation of a line is y = -1/2x + 3, what is the x-intercept?
Solution
To find the x-intercept, set y = 0. The equation becomes 0 = -1/2x + 3, leading to x = 6.
Correct Answer:
A
— 6
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Q. If the equation of a line is y = -1/2x + 3, what is the y-value when x = 4?
Solution
Substituting x = 4 into the equation gives y = -1/2(4) + 3 = -2 + 3 = 1.
Correct Answer:
B
— 2
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Q. If the equation of a line is y = mx + c, what does 'm' represent?
-
A.
The y-intercept
-
B.
The slope
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C.
The x-intercept
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D.
The distance
Solution
'm' in the equation of a line represents the slope, which indicates the steepness and direction of the line.
Correct Answer:
B
— The slope
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Q. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what are the coordinates of the other endpoint?
-
A.
(6, 7)
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B.
(8, 9)
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C.
(4, 5)
-
D.
(0, 1)
Solution
Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.
Correct Answer:
A
— (6, 7)
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Q. If the midpoint of a line segment is (4, 5) and one endpoint is (2, 3), what is the other endpoint?
-
A.
(6, 7)
-
B.
(8, 9)
-
C.
(4, 5)
-
D.
(2, 3)
Solution
Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.
Correct Answer:
A
— (6, 7)
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Q. If the midpoint of a line segment joining points A(1, 2) and B(x, y) is M(3, 4), what is the value of x?
Solution
The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2). Setting up the equations: (1 + x)/2 = 3 gives x = 5.
Correct Answer:
B
— 6
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Q. In a coordinate plane, if the point A(2, 3) is reflected across the x-axis, what are the coordinates of the reflected point?
-
A.
(2, -3)
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B.
(3, 2)
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C.
(-2, 3)
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D.
(3, -2)
Solution
Reflecting a point across the x-axis changes the sign of the y-coordinate. Thus, A(2, 3) becomes (2, -3).
Correct Answer:
A
— (2, -3)
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Q. In a coordinate plane, if the point A(2, 3) is reflected over the x-axis, what are the coordinates of the reflected point?
-
A.
(2, -3)
-
B.
(3, 2)
-
C.
(-2, 3)
-
D.
(-3, -2)
Solution
Reflecting a point (x, y) over the x-axis results in (x, -y). Therefore, A(2, 3) becomes (2, -3).
Correct Answer:
A
— (2, -3)
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Q. In a triangle formed by the points A(1, 2), B(4, 6), and C(1, 6), which of the following statements is true?
-
A.
AB is parallel to AC
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B.
AB is perpendicular to AC
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C.
AC is longer than AB
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D.
All sides are equal
Solution
The slope of AB is (6-2)/(4-1) = 4/3, and the slope of AC is (6-2)/(1-1) which is undefined. Since one slope is undefined, AB is perpendicular to AC.
Correct Answer:
B
— AB is perpendicular to AC
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Q. What is the area of a triangle formed by the points (0, 0), (4, 0), and (0, 3)?
Solution
The area of a triangle is given by (1/2) * base * height. Here, base = 4 and height = 3, so area = (1/2) * 4 * 3 = 6.
Correct Answer:
A
— 6
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Q. What is the distance between the points (1, 1) and (4, 5)?
Solution
Using the distance formula, d = √[(x2 - x1)² + (y2 - y1)²] = √[(4 - 1)² + (5 - 1)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.
Correct Answer:
C
— 5
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Q. What is the distance between the points P(3, 4) and Q(7, 1) in the coordinate plane?
Solution
Using the distance formula d = √((x2 - x1)² + (y2 - y1)²), we find d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.
Correct Answer:
B
— 6
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Q. What is the distance between the points P(3, 4) and Q(7, 1)?
Solution
Using the distance formula, d = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the equation of a line that passes through the origin and has a slope of 4?
-
A.
y = 4x
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B.
y = x/4
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C.
y = 4/x
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D.
y = 1/4x
Solution
The equation of a line in slope-intercept form is y = mx + b. Since it passes through the origin, b = 0, thus y = 4x.
Correct Answer:
A
— y = 4x
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Q. Which of the following equations represents a circle with a center at (0, 0) and a radius of 5?
-
A.
x^2 + y^2 = 5
-
B.
x^2 + y^2 = 25
-
C.
x^2 - y^2 = 25
-
D.
x^2 + y^2 = 10
Solution
The standard equation of a circle with center (0, 0) and radius r is x^2 + y^2 = r^2. Here, r = 5, so r^2 = 25.
Correct Answer:
B
— x^2 + y^2 = 25
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Q. Which of the following equations represents a circle with a center at (3, -2) and a radius of 5?
-
A.
(x - 3)² + (y + 2)² = 25
-
B.
(x + 3)² + (y - 2)² = 25
-
C.
(x - 3)² + (y - 2)² = 25
-
D.
(x + 3)² + (y + 2)² = 25
Solution
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Correct Answer:
A
— (x - 3)² + (y + 2)² = 25
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Q. Which of the following equations represents a line parallel to y = -3x + 4?
-
A.
y = -3x + 1
-
B.
y = 3x - 4
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C.
y = -x + 2
-
D.
y = 2x + 3
Solution
Parallel lines have the same slope. The slope of y = -3x + 4 is -3, so any line with the same slope, like y = -3x + 1, is parallel.
Correct Answer:
A
— y = -3x + 1
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Q. Which of the following points is closest to the origin (0, 0)?
-
A.
(1, 1)
-
B.
(2, 2)
-
C.
(3, 3)
-
D.
(0, 1)
Solution
The distance from the origin to a point (x, y) is given by √(x² + y²). The point (0, 1) has a distance of 1, which is the smallest.
Correct Answer:
D
— (0, 1)
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Q. Which of the following points is equidistant from the points (1, 2) and (3, 4)?
-
A.
(2, 3)
-
B.
(4, 5)
-
C.
(0, 1)
-
D.
(1, 1)
Solution
The point (2, 3) is the midpoint of the segment joining (1, 2) and (3, 4), making it equidistant from both.
Correct Answer:
A
— (2, 3)
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Q. Which of the following points lies on the line represented by the equation y = 2x + 1?
-
A.
(0, 1)
-
B.
(1, 2)
-
C.
(2, 5)
-
D.
(3, 6)
Solution
Substituting x = 2 into the equation y = 2(2) + 1 gives y = 5, so the point (2, 5) lies on the line.
Correct Answer:
C
— (2, 5)
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