GRE Quantitative Quiz: Coordinate Geometry Distance
Practice Coordinate Geometry Distance in GRE Quantitative with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
What this quiz covers
This quiz focuses on Coordinate Geometry Distance, giving you a quick way to practice the rules, question types, and explanations that matter most for GRE Quantitative.
How to use this quiz
Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.
Question 1
Points R(−2,1) and S(4,4) lie in the coordinate plane. What is the distance between R and S?
9
45
Explanation: This question tests coordinate geometry distance between two points. The distance formula states that d = √[(x₂-x₁)² + (y₂-y₁)²] for points (x₁, y₁) and (x₂, y₂). For points R(-2, 1) and S(4, 4), we calculate: d = √[(4-(-2))² + (4-1)²] = √[(6)² + (3)²] = √[36 + 9] = √45. The distance between R and S is √45, which corresponds to choice B. Note that √45 can be simplified to 3√5, but this simplified form doesn't appear in the choices. Choice A (9) represents the sum of absolute differences |6| + |3|, which is the Manhattan distance, not the Euclidean distance.
Question 2
In the coordinate plane, point T is at (4,0) and point U is at (−2,−3). What is the distance between and ?
Question 3
Points P(−2,3) and Q(4,−1) lie in the coordinate plane. What is the distance between P and ?
Question 4
Points L(−3,4) and M(1,−2) lie in the coordinate plane. What is the distance between L and ?
Question 5
In the coordinate plane, point R is at (−4,7) and point S is at (−4,−. What is the distance between and ?
Question 6
In the coordinate plane, point M is at (0,−3) and point N is at (6,−3). What is the distance between and ?
Question 7
In the coordinate plane, point A is at (2,5) and point B is at (8,1). What is the distance between and ?
Question 8
In the coordinate plane, point C is at (3,1) and point D is at (−1,4). Which of the following equals the distance from to ?
Question 9
Points P(1,1) and Q(4,5) lie in the coordinate plane. What is the distance between P and ?
Question 10
In the coordinate plane, point W is at (−1,2) and point X is at (3,−1). What is the distance between and ?
Question 11
Points J(2,−1) and K(−4,7) lie in the coordinate plane. What is the distance between J and ?
Question 12
In the coordinate plane, point L is at (4,0) and point M is at (0,3). What is the distance between and ?
Question 13
Points E(2,−4) and F(2,3) lie in the coordinate plane. What is the distance between E and ?
Question 14
In the coordinate plane, point J is at (−3,2) and point K is at (1,−4). Which of the following is the distance between and ?
Question 15
Points Y(0,0) and Z(6,8) lie in the coordinate plane. Which of the following equals the distance from Y to ?
Question 16
In the coordinate plane, point G is at (5,−1) and point H is at (−1,−5. Which of the following equals the distance from to ?
Question 17
Points U(−2,−2) and V(3,4) lie in the coordinate plane. Which of the following equals the distance from U to ?
Question 18
Points E(−3,−5) and F(1,0) lie in the coordinate plane. What is the distance between E and ?
Question 19
In the coordinate plane, point P is at (−2,3) and point Q is at (4,−1). Which of the following is the distance from to ?
Question 20
In the coordinate plane, point G is at (1,−2) and point H is at (7,1). What is the distance between and ?
13
45
39
T
U
45
9
45
27
9
Explanation: This question tests coordinate geometry distance between two points. The distance formula states that for points (x1,y1) and (x2,y2), the distance is d=(x2−x1). For T(4,0) and U(−2,−3), we substitute: d=(−2−4)2+(−3−0. This gives us d=36+9=45. The distance is 45, which can also be simplified to 35 but this form is not among the choices. The Manhattan distance would be ∣4−(−2)∣+∣0−(−3)∣=6+3=9, which appears as choice B but is incorrect for Euclidean distance.
Q
52
40
10
52
10
Explanation: This question tests coordinate geometry distance between two points. The distance formula states that for points (x1,y1) and (x2,y2), the distance is d=(x2−x1). For P(−2,3) and Q(4,−1), we substitute: d=(4−(−2))2+(−1. This gives us d=62+(−4)2. The correct answer is 52. A common error would be to calculate the Manhattan distance as ∣4−(−2)∣+∣−1−3∣=6+4=10, but this is not the Euclidean distance.
M
20
10
52
52
10
Explanation: This question tests the distance formula in coordinate geometry. For two points (x1,y1) and (x2,y2), the distance is d=(x2−x1). With L(−3,4) and M(1,−2), we calculate: d=(1−(−3))2+(−2. This gives us d=42+36=. The correct answer is 52. The Manhattan distance would be ∣1−(−3)∣+∣−2−4∣=4+6=10, which appears as choice B but is incorrect for Euclidean distance.
2
)
R
S
9
81
9
13
13
Explanation: This question tests coordinate geometry distance calculation. The distance formula for points (x1,y1) and (x2,y2) is d=(x2−x1). For R(−4,7) and S(−4,−2), notice both points have the same x-coordinate of -4, forming a vertical line segment. The distance is d=(−4−(−4))2+(−2. Since the points lie on a vertical line, the distance equals the absolute difference of y-coordinates: ∣7−(−2)∣=∣7+2∣=9. Choice B (81) represents the square of the distance before taking the square root, while choice D (13) might result from incorrectly adding 4 + 9.
M
N
36
36
0
6
6
Explanation: This question tests the distance formula in coordinate geometry. The distance between points (x1,y1) and (x2,y2) is d=(x2−x1). For M(0,−3) and N(6,−3), notice that both points have the same y-coordinate of -3, making this a horizontal line segment. The distance is d=(6−0)2+(−3−(−3. Since the points lie on a horizontal line, the distance is simply the difference in x-coordinates: ∣6−0∣=6. Choice A (36) represents the square of the distance, while choice B (36) is another way to write 6.
A
B
52
10
52
20
8
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points A(2,5) and B(8,1), the difference in x-coordinates is 8 - 2 = 6, and the difference in y-coordinates is 1 - 5 = -4. Squaring these gives 36 and 16, and adding them results in 52. Taking the square root yields √52, which matches choice A. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |6| + |4| = 10, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
C
D
25
7
25
7
17
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points C(3,1) and D(-1,4), the difference in x-coordinates is -1 - 3 = -4, and the difference in y-coordinates is 4 - 1 = 3. Squaring these gives 16 and 9, and adding them results in 25. Taking the square root yields √25, which matches choice A. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |4| + |3| = 7, appearing as choice D, but this measures grid path distance, not the straight-line Euclidean distance required here.
Q
7
25
25
7
5
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points P(1,1) and Q(4,5), the difference in x-coordinates is 4 - 1 = 3, and the difference in y-coordinates is 5 - 1 = 4. Squaring these gives 9 and 16, and adding them results in 25. Taking the square root yields √25 = 5, which matches choice E. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |3| + |4| = 7, appearing as choice D, but this measures grid path distance, not the straight-line Euclidean distance required here.
W
X
25
7
5
25
13
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points W(-1,2) and X(3,-1), the difference in x-coordinates is 3 - (-1) = 4, and the difference in y-coordinates is -1 - 2 = -3. Squaring these gives 16 and 9, and adding them results in 25. Taking the square root yields √25 = 5, which matches choice C. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |4| + |3| = 7, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
K
28
14
100
100
10
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points J(2,-1) and K(-4,7), the difference in x-coordinates is -4 - 2 = -6, and the difference in y-coordinates is 7 - (-1) = 8. Squaring these gives 36 and 64, and adding them results in 100. Taking the square root yields √100 = 10, which matches choice E. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |6| + |8| = 14, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
L
M
7
7
25
25
5
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points L(4,0) and M(0,3), the difference in x-coordinates is 0 - 4 = -4, and the difference in y-coordinates is 3 - 0 = 3. Squaring these gives 16 and 9, and adding them results in 25. Taking the square root yields √25 = 5, which matches choice E. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |4| + |3| = 7, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
F
49
7
49
1
7
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points E(2,-4) and F(2,3), the difference in x-coordinates is 2 - 2 = 0, and the difference in y-coordinates is 3 - (-4) = 7. Squaring these gives 0 and 49, and adding them results in 49. Taking the square root yields √49 = 7, which matches choice B. In this vertical case, the Manhattan distance also equals 7, but a common error might be using √7 (choice E), perhaps from mistakenly squaring only part of the difference.
J
K
52
10
20
52
8
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points J(-3,2) and K(1,-4), the difference in x-coordinates is 1 - (-3) = 4, and the difference in y-coordinates is -4 - 2 = -6. Squaring these gives 16 and 36, and adding them results in 52. Taking the square root yields √52, which matches choice A. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |4| + |6| = 10, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
Z
28
14
100
100
10
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points Y(0,0) and Z(6,8), the difference in x-coordinates is 6 - 0 = 6, and the difference in y-coordinates is 8 - 0 = 8. Squaring these gives 36 and 64, and adding them results in 100. Taking the square root yields √100 = 10, which matches choice E. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |6| + |8| = 14, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
)
G
H
52
10
52
20
8
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points G(5,-1) and H(-1,-5), the difference in x-coordinates is -1 - 5 = -6, and the difference in y-coordinates is -5 - (-1) = -4. Squaring these gives 36 and 16, and adding them results in 52. Taking the square root yields √52, which matches choice A. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |6| + |4| = 10, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
V
61
11
61
25
11
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points U(-2,-2) and V(3,4), the difference in x-coordinates is 3 - (-2) = 5, and the difference in y-coordinates is 4 - (-2) = 6. Squaring these gives 25 and 36, and adding them results in 61. Taking the square root yields √61, which matches choice A. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |5| + |6| = 11, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
F
41
9
41
25
13
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points E(-3,-5) and F(1,0), the difference in x-coordinates is 1 - (-3) = 4, and the difference in y-coordinates is 0 - (-5) = 5. Squaring these gives 16 and 25, and adding them results in 41. Taking the square root yields √41, which matches choice A. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |4| + |5| = 9, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
P
Q
52
10
52
40
6
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points P(-2,3) and Q(4,-1), the difference in x-coordinates is 4 - (-2) = 6, and the difference in y-coordinates is -1 - 3 = -4. Squaring these gives 36 and 16, and adding them results in 52. Taking the square root yields √52, which matches choice A. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |6| + |4| = 10, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.
G
H
45
9
45
27
9
Explanation: This question tests the concept of distance in coordinate geometry. The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2 - x1)² + (y2 - y1)²]. For points G(1,-2) and H(7,1), the difference in x-coordinates is 7 - 1 = 6, and the difference in y-coordinates is 1 - (-2) = 3. Squaring these gives 36 and 9, and adding them results in 45. Taking the square root yields √45, which matches choice A. A tempting incorrect option is the Manhattan distance, which adds the absolute differences |6| + |3| = 9, appearing as choice B, but this measures grid path distance, not the straight-line Euclidean distance required here.