Q. If a circle is centered at (0, 0) with a radius of 5, which of the following points lies outside the circle?
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A.
(3, 4)
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B.
(0, 5)
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C.
(5, 0)
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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 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 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 y = mx + c, what does 'm' represent?
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A.
The y-intercept
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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?
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A.
(6, 7)
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B.
(8, 9)
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C.
(4, 5)
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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?
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A.
(6, 7)
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B.
(8, 9)
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C.
(4, 5)
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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. In a coordinate plane, if the point A(2, 3) is reflected across the x-axis, what are the coordinates of the reflected point?
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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?
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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 (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. 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. Which of the following equations represents a circle with a center at (0, 0) and a radius of 5?
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A.
x^2 + y^2 = 5
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B.
x^2 + y^2 = 25
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C.
x^2 - y^2 = 25
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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 line parallel to y = -3x + 4?
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A.
y = -3x + 1
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B.
y = 3x - 4
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C.
y = -x + 2
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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)?
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A.
(1, 1)
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B.
(2, 2)
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C.
(3, 3)
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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 lies on the line represented by the equation y = 2x + 1?
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A.
(0, 1)
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B.
(1, 2)
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C.
(2, 5)
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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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Q. Which of the following statements is true regarding the points (2, 3), (4, 5), and (6, 7)?
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A.
They are collinear
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B.
They form a triangle
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C.
They are equidistant
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D.
They lie on different lines
Solution
The slope between any two pairs of these points is the same (1), indicating they are collinear.
Correct Answer: A — They are collinear
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