Equation of a Line

Distance & Midpoint

A robot moves at a constant speed along a straight-line path from one point to another point. The starting point, midpoint, and stopping point are represented in the standard (x,y) coordinate plane. Given that the midpoint is represented by (24,32) and the stopping point is represented by (24,37), which of the following coordinates represents the starting point of the robot?

2026 April(R4A) Math Question 4

5. For ↔RT shown below, point S is on RT, the length of RS is 10 cm, and the length of ST is 18 cm. What is the distance, in centimeters, between T and the midpoint of RS ?

2021 April(D05) Math Question 5

8. When points A and B(-3,4) are graphed in the standard (x,y) coordinate plane below, the midpoint of AB will be (1,2). What will be the coordinates of point A ?

2015 June(73C) Math Question 8

9. In the standard (x,y) coordinate plane, what is the midpoint of the line segment that has endpoints (3,8) and (1,-4) ?

2017 April(74F) Math Question 9

9. On a bike trail there 'are 5 2heckpoints numbered in
order, Checkpoint 1 through Checkpoint 5,.as shown in
the figure below. Some di!ltances along the trail
between 2 checkpoints are given: 6.6 miles between
1 and 3; 4.5 miles between 2 and 3; and 9.7 miles
betwe~ri 2 and 5. Which .of the following values is
closest to the distance, in miles, along the tr.ail between
Checkpoint 1 and Checkpoint 5 ?

2019 June(B02) Math Question 9

10. On the real number line, point J is at —7 and point K is at —14. What is the distance between J and K ?

2015 April(73G) Math Question 10

2019 June(72F) Math Question 11

12. In the standard (x,y) coordinate plane, the point (2,1) is the midpoint of CD. Point  C has coordinates (6,8). What are the coordinates of point D ?

2021 April(Z04) Math Question 12

13. In the standard (x,y) coordinate plane, the point (3,-7) is the midpoint of the line segment with endpoints (9, -11) and:

2018 April(A09) Math Question 13

2009 December(68A) Math Question 13

2012 April(70G) Math Question 13

15. The straight-line distance, in miles, from Marville to Bright City must be:

2014 April(71H) Math Question 15

2012 June(70C) Math Question 16

2019 December(C03) Math Question 17

2013 December(71E) Math Question 17

17. In the standard (x,y) coordinate plane, the midpoint of AB is at (2,1), and A is at (8,10). What is the x-coordinate of B ?

2018 June(A11) Math Question 17

2011 June(69F) Math Question 19

19. In the standard (x,y) coordinate plane, the point (2,-4) is the midpoint of the line segment with endpoints (8,-8) and:

2015 April(73G) Math Question 19

2009 December(68A) Math Question 21

2020 July(C01) Math Question 21

22. For AC shown below, B is on AC, the length of AB is 12 cm, and the length of BC is 20 cm. What is the distance, in centimeters, between C and the midpoint

2013 June(71C) Math Question 22

22. As shown below, A, B, C, and D are collinear, with B between A and C and with C between B and D. Given AC = BD = 12 cm and given BC = 3 cm, what is AD, in centimeters?

2016 April(73E) Math Question 22

2010 June(68C) Math Question 24

24. What rational number is exactly halfway between 3/16 and 7/32 on the real number line?

Number Line

2021 April(D05) Math Question 24

24. What is the length, in coordinate units, of the line segment with endpoints (-8,4) and (4,9) in the standard (x,y) coordinate plane?

2015 December(72E) Math Question 24

2011 April(67F) Math Question 28

28. On Friday night, the Morrison family set up camp in the Ocala National Forest. On Saturday morning they hiked to a wilderness area 3 miles due north and 4 miles due east of their campsite. The elevation of the wilderness area is the same as the elevation of the campsite. To the nearest 0.1 mile, what is the straight-line distance from the wilderness area to the Morrisons' campsite?

2016 April(73E) Math Question 28

28. In the standard (x,y) coordinate plane, what is the distance, in coordinate units, from A(5 1/3,-3) to B(-1 5/9 ,−3) ?

Distance formula (distance between 2 points, vertical distance, horizontal distance)

2020 December(D03) Math Question 28

30. What is the distance, in coordinate units, from B to D ?

2017 June(74C) Math Question 30

2010 December(69A) Math Question 31

2019 December(C03) Math Question 31

34. Whatis the length of AB in coordinate units?

2019 June(B02) Math Question 34

34. What rational number is exactly halfway between and on the real number line?

Midpoint Formula

2020 December(D03) Math Question 34

35. Students and adults from Western High School visited an amusement park on a field trip. The amusement park charged $25 for each adult ticket and $20 for each student ticket. Before the trip, the students were given this information about the Happy Dragon roller coaster: the average speed of the roller coaster is 50 miles per hour, and 1 ride on the roller coaster track is completed in 2.25 minutes. A graph showing the height above level ground, in feet, with respect to the time into the ride, in seconds, is given below. Which of the following values is closest to the total distance traveled, in miles, during 1. complete ride on the roller coaster track?

2018 April(A09) Math Question 35

2010 December(69A) Math Question 35

2013 December(71E) Math Question 36

37. Which of the following values is closest to the distance, in inches, between point A and point B on the ruler shown below? (Note: The ruler shown is NOT actual size.)
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2014 December(72G) Math Question 37

2020 July(C01) Math Question 37

2009 April(66F) Math Question 38

2012 December(71A) Math Question 39

2009 April(66F) Math Question 39

39. Point A lies at (2,6) and point B lies at (-5,10) in the standard (x,y) coordinate plane below. What is the length, in coordinate units, of AB ?

2016 April(73E) Math Question 39

2009 December(68A) Math Question 39

2009 June(67C) Math Question 39

2012 June(70C) Math Question 40

2010 December(69A) Math Question 41

2015 December(72E) Math Question 42

42. In the standard (x,y) coordinate plane, the 3 distinct points A(3,5), B(6,8), and C are collinear, and B is equidistant from A and C. What are the coordinates of C?

2020 December(D03) Math Question 42

2010 April(68G) Math Question 44

2019 June(72F) Math Question 46

2012 April(70G) Math Question 46

2011 June(69F) Math Question 46

2010 June(68C) Math Question 47

2019 April(Z15) Math Question 47

48. A square in the standard (x,y) coordinate plane has vertices at (1,3), (2,1), (4,2), and (3,4). Where do the diagonals of the square intersect?

2014 June(72C) Math Question 48

2020 June(C02) Math Question 52

2010 April(68G) Math Question 54

2010 June(68C) Math Question 56

57. In the standard (x,y) coordinate plane, define the h−v distance between 2 points to be the length, in coordinate units, of the shortest path between the 2 points using only horizontal and vertical segments. The expression ⎪5 − 2⎪ + ⎪3 − (−4)⎪ gives the h−v distance between which of the following pairs of points?

Distance & MidpointEquation of a LineACT math questions

2026 April(R4A) Math Question 4

2021 April(D05) Math Question 5