Q. What is the distance between the points (-1, -1) and (3, 3)?
A.
4.24
B.
5.66
C.
6.0
D.
7.0
Show solution
Solution
Using the distance formula: d = √((3 - (-1))² + (3 - (-1))²) = √(16 + 16) = √32 = 4√2 ≈ 5.66.
Correct Answer:
B
— 5.66
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Q. What is the distance between the points (-2, -3) and (2, 1)?
A.
5.66
B.
6.32
C.
4.47
D.
5.0
Show solution
Solution
Using the distance formula: d = √((2 - (-2))² + (1 - (-3))²) = √(16 + 16) = √32 = 4√2 ≈ 5.66.
Correct Answer:
A
— 5.66
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Q. What is the distance between the points (0, 0) and (5, 12)?
A.
12.5
B.
13.0
C.
11.0
D.
10.0
Show solution
Solution
Using the distance formula: d = √((5 - 0)² + (12 - 0)²) = √(25 + 144) = √169 = 13.0.
Correct Answer:
B
— 13.0
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Q. What is the distance between the points (0, 0) and (x, y) if the distance is 10?
A.
x² + y² = 100
B.
x² + y² = 10
C.
x² + y² = 50
D.
x² + y² = 25
Show solution
Solution
Using the distance formula: d = √(x² + y²) = 10 implies x² + y² = 100.
Correct Answer:
A
— x² + y² = 100
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Q. What is the distance between the points (1, 1) and (1, 5)?
Show solution
Solution
Using the distance formula: d = √((1 - 1)² + (5 - 1)²) = √(0 + 16) = √16 = 4.
Correct Answer:
A
— 4
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Q. What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?
Show solution
Solution
Using the distance formula d = √((x2 - x1)² + (y2 - y1)²), we find d = √((4 - 1)² + (6 - 2)²) = √(9 + 16) = √25 = 5.
Correct Answer:
B
— 5
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Q. What is the distance between the points (2, 3) and (5, 7) in a coordinate plane?
Show solution
Solution
Distance = √((x2 - x1)² + (y2 - y1)²) = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance between the points (2, 3) and (5, 7) in the coordinate plane?
Show solution
Solution
Distance = √((5-2)² + (7-3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance between the points (3, 4) and (3, 10) in the coordinate plane?
Show solution
Solution
The distance formula gives d = |y2 - y1| = |10 - 4| = 6.
Correct Answer:
A
— 6
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Q. What is the distance between the points (3, 4) and (7, 1) in the coordinate plane?
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Solution
Distance = √((7-3)² + (1-4)²) = √(4 + 9) = √13 ≈ 3.6.
Correct Answer:
A
— 5
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Q. What is the distance between the points (5, 5) and (5, 1)?
A.
4.0
B.
5.0
C.
3.0
D.
2.0
Show solution
Solution
Using the distance formula: d = √((5 - 5)² + (1 - 5)²) = √(0 + 16) = √16 = 4.0.
Correct Answer:
A
— 4.0
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Q. What is the distance between the points (5, 5) and (5, 10)?
A.
5.0
B.
10.0
C.
15.0
D.
0.0
Show solution
Solution
Using the distance formula: d = √((5 - 5)² + (10 - 5)²) = √(0 + 25) = √25 = 5.0.
Correct Answer:
A
— 5.0
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Q. What is the distance between the points (5, 5) and (5, 9)?
Show solution
Solution
Using the distance formula: d = √((5 - 5)² + (9 - 5)²) = √(0 + 16) = √16 = 4.
Correct Answer:
A
— 4
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Q. What is the distance from the point (1, -1) to the line 2x + 3y - 6 = 0?
Show solution
Solution
Distance = |Ax1 + By1 + C| / √(A² + B²) = |2*1 + 3*(-1) - 6| / √(2² + 3²) = |-7| / √13 = 7/√13.
Correct Answer:
A
— 2
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Q. What is the distance from the point (1, 2) to the line 3x + 4y - 12 = 0?
Show solution
Solution
Distance = |Ax1 + By1 + C| / √(A² + B²) = |3(1) + 4(2) - 12| / √(3² + 4²) = |3 + 8 - 12| / 5 = | -1 | / 5 = 1/5.
Correct Answer:
B
— 3
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Q. What is the distance from the point (2, -3) to the line 3x + 4y - 12 = 0?
A.
2.5
B.
3.0
C.
4.0
D.
5.0
Show solution
Solution
Distance from point (x0, y0) to line Ax + By + C = 0 is given by |Ax0 + By0 + C| / √(A² + B²). Here, A=3, B=4, C=-12. Distance = |3*2 + 4*(-3) - 12| / √(3² + 4²) = |6 - 12 - 12| / 5 = 3.0.
Correct Answer:
B
— 3.0
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Q. What is the distance from the point (2, 3) to the line 2x + 3y - 6 = 0?
Show solution
Solution
Distance = |Ax1 + By1 + C| / √(A² + B²) = |2(2) + 3(3) - 6| / √(2² + 3²) = |4 + 9 - 6| / √13 = 7 / √13 ≈ 1.94, which rounds to 2.
Correct Answer:
B
— 2
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Q. What is the distance from the point (2, 3) to the line defined by the equation 2x + 3y - 6 = 0?
Show solution
Solution
Distance = |Ax + By + C| / √(A² + B²) = |2(2) + 3(3) - 6| / √(2² + 3²) = |4 + 9 - 6| / √13 = 7/√13.
Correct Answer:
A
— 1
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Q. What is the distance from the point (3, 2) to the line 2x + 3y - 6 = 0?
Show solution
Solution
Distance from point (x0, y0) to line Ax + By + C = 0 is given by |Ax0 + By0 + C| / √(A² + B²). Here, A=2, B=3, C=-6. Distance = |2*3 + 3*2 - 6| / √(2² + 3²) = |6 + 6 - 6| / √(4 + 9) = 6 / √13 ≈ 1.67, which rounds to 2.
Correct Answer:
B
— 2
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Q. What is the distance from the point (3, 4) to the line defined by the equation 2x + 3y - 12 = 0?
Show solution
Solution
Using the formula for distance from a point to a line: d = |Ax + By + C| / √(A² + B²), where A=2, B=3, C=-12. d = |2*3 + 3*4 - 12| / √(2² + 3²) = |6 + 12 - 12| / √13 = 6/√13.
Correct Answer:
A
— 2
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Q. What is the distance from the point (3, 4) to the line defined by the equation 2x + 3y - 6 = 0?
A.
2.0
B.
1.0
C.
3.0
D.
4.0
Show solution
Solution
Distance = |Ax1 + By1 + C| / √(A² + B²) = |2*3 + 3*4 - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13 ≈ 1.0.
Correct Answer:
B
— 1.0
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Q. What is the equation of a circle with center at (0, 0) and radius 3?
A.
x² + y² = 9
B.
x² + y² = 3
C.
x² + y² = 6
D.
x² + y² = 12
Show solution
Solution
The standard form is (x - h)² + (y - k)² = r². Here, h=0, k=0, r=3, so the equation is x² + y² = 3² = 9.
Correct Answer:
A
— x² + y² = 9
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Q. What is the equation of a circle with center at (0, 0) and radius 4?
A.
x² + y² = 16
B.
x² + y² = 8
C.
x² + y² = 4
D.
x² + y² = 20
Show solution
Solution
The equation of a circle is (x - h)² + (y - k)² = r². Here, h = 0, k = 0, r = 4, so x² + y² = 4² = 16.
Correct Answer:
A
— x² + y² = 16
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Q. What is the equation of a circle with center at (0, 0) and radius 5?
A.
x² + y² = 25
B.
x² + y² = 5
C.
x² + y² = 10
D.
x² + y² = 20
Show solution
Solution
The equation of a circle is (x - h)² + (y - k)² = r². Here, h=0, k=0, r=5, so x² + y² = 5² = 25.
Correct Answer:
A
— x² + y² = 25
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Q. What is the equation of a circle with center at (1, 1) and radius 2?
A.
(x - 1)² + (y - 1)² = 4
B.
(x + 1)² + (y + 1)² = 4
C.
(x - 1)² + (y - 1)² = 2
D.
(x - 1)² + (y - 1)² = 8
Show solution
Solution
The equation of a circle is (x - h)² + (y - k)² = r². Here, r = 2, so (x - 1)² + (y - 1)² = 2² = 4.
Correct Answer:
A
— (x - 1)² + (y - 1)² = 4
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Q. What is the equation of a line parallel to y = -3x + 2 that passes through the point (1, 4)?
A.
y = -3x + 7
B.
y = 3x + 1
C.
y = -3x + 1
D.
y = 3x - 1
Show solution
Solution
Parallel lines have the same slope. The slope is -3. Using point-slope form: y - 4 = -3(x - 1) gives y = -3x + 7.
Correct Answer:
A
— y = -3x + 7
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Q. What is the equation of a line parallel to y = -3x + 4 that passes through the point (2, 1)?
A.
y = -3x + 7
B.
y = 3x - 5
C.
y = -3x + 1
D.
y = 3x + 1
Show solution
Solution
The slope of the line is -3. Using point-slope form: y - 1 = -3(x - 2) gives y = -3x + 7.
Correct Answer:
A
— y = -3x + 7
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Q. What is the equation of a line parallel to y = 3x + 2 that passes through the point (1, 1)?
A.
y = 3x - 2
B.
y = 3x + 1
C.
y = 3x + 3
D.
y = 3x + 2
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 1 = 3(x - 1) gives y = 3x - 2.
Correct Answer:
B
— y = 3x + 1
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Q. What is the equation of a line that passes through the points (1, 2) and (3, 6)?
A.
y = 2x
B.
y = 3x - 1
C.
y = 2x + 1
D.
y = x + 1
Show solution
Solution
Slope = (6-2)/(3-1) = 2. Using point-slope form: y - 2 = 2(x - 1) gives y = 2x.
Correct Answer:
A
— y = 2x
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Q. What is the equation of a line with a slope of 2 that passes through the point (1, 3)?
A.
y = 2x + 1
B.
y = 2x + 3
C.
y = 2x - 1
D.
y = 2x - 3
Show solution
Solution
Using point-slope form: y - y1 = m(x - x1) => y - 3 = 2(x - 1) => y = 2x + 1.
Correct Answer:
B
— y = 2x + 3
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