Distance & Midpoint Formula

Distance

100

What is the distance formula?

d=√(x₂-x₁)²+(y₂-y₁)²

200

What is the distance between (8,11) and (8,4)?

7

300

Find the distance between the points (3, 8) and (3, -6).

14 units

400

Find the distance between the points (4, 1) and (7, 5). 

5 units

500

What is the distance from (2, 3) to the origin?

√13

Midpoint

100

What is the midpoint formula?

M(((x₁+x₂)/2),((y₁+y₂)/2)))

200

Given the points A and B where A is at coordinates (1,-5) and B is at coordinates (-3,-7) on the line segment AB, find the midpoint of AB.

(-2,-6)

300

Find the midpoint of the line segment AB where point A is at (-4, -11) and point B is at (-6, -3).

(-5,-7)

400

Find the midpoint of the line segment joining the points (1, -4) and (-5, 2)

(-2,-1)

500

Tommy is at Disneyland taking pictures with the characters. If SpongeBob is at (-8,3) and Mickey Mouse is at (2,-5), and Tommy is sitting between them, where is Tommy located at?

(-3,-1)

Distance Word Problems

100

Amy, and Ella are playing jump rope. Amy is standing at (5,6) and Ella is standing at (2,5). What is the distance between them?

√10 

200

The teacher stands at (4,2) and a student is sitting at (2,2). What is the distance between the teacher and students?

2

300

Tommy's phone is ringing in the bedroom,(4,7), but he is in the living room,(-2,-1). What is the distance Tommy needs to go to pick up his phone?

10

400

On a map’s coordinate grid, Blue City is located at (-2, 0) and Red Ville is located at (1, 4). How long is the train’s route if it travels along a straight line from Blue City to Red Ville?

5 units

500

Find the distance of the point (-6, 3) from the origin.

3√5

Midpoint Word Problems

100

Cindy was standing in between KFC and McDonalds. If McDonald is located at (4,8) and KFC is located at (-10,-8), where is Cindy located at?

(-3,0)

200

Two ships started at the same point and steamed in opposite directions at the same speed. After one hour, Ship X was at point (16, 23) while Ship Y is at (22,-15). At what point did they start?

(19, 4)

300

Henry just got out of school and he can either go to the library or to the mall. If the two places are equidistance from the school, the mall is at (9,2) and the library is at (-3,6), where is the school located at?

(3, 4)

400

A line segment whose midpoint is (-1, 0) has an endpoint of (-4, -3). What is the other endpoint?

(2, 3)

500

Lily is deciding between dessert or Teaway. Teaway is at (6,6) and the dessert house is at (9,-3). If Lily is standing in between them, where is she?

(7.5, 1.5)