Distance, Midpoint, Ratios

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

Given the points A and B where A is at coordinates ( 2, -5 ) and B is at coordinates ( -3, -7 ) on the line segment AB, find the length of AB.

√29 or 5.39

400

Classify triangle ABC as scalene, isosceles, or equilateral A(3,1), B(4,2), C(1,3)

scalene

500

Classify triangle ABC as scalene, isosceles, or equilateral A(-4,3), B(4,3), C(0,4)

isosceles

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 ( 2,-5 ) and B is at coordinates ( -3,-7 ) on the line segment AB, find the midpoint of AB.

(-.5,-6)

300

Find the midpoint of the line segment AB where point A is at ( 0, 2 ) and point B is at ( -1, - 4 ).

(-.5,-1)

400

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

(-1.5,-1)

500

Write an equation for the perpendicular bisector of the line segment joining A(-1, 4) and B(5, 2)

y=3x-3

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 or 3.16

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,(8,2). What is the distance Tommy needs to go to pick up his phone?

√41 or 6.4

400

To get from his home to his girlfriend's home, Jimmy must drive around the library. If he drives 3 miles north, then 4 miles east, and finally 5 miles south, what is the straight-line distance between Jimmy's home and his girlfriend's home?

√20 or 4.47

500

A skydiver lands 150 yards west and 30 yards north of a target. A second skydiver lands 45 yards east and 150 yards south of the same target. How far from each other did the two skydivers land?

√70425 or 265.38

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

Sharon is standing at (5,8) when two cars from the same distance is driving towards her. One of the car is located at (-1, 3), where is the other car located at?

(11,13)

300

Henry just got out of school and he can either go to the library or to the mall. If the two places are equidistances from the school, the mall is at (9,2) and the school is at (3,4), where is the library located at?

(-3,6)

400

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)

500

Lily is deciding between dessert or Teaway. Teaway is at (5,6) and the dessert house is at (9,-3). If Lily is standing in between them, where is she?

(7,1.5)

Partition by Ratio

100

Given points A(1, 3) and B(7, 9), find the point P that divides the line segment AB in a ratio of 2:3.

(3.4, 5.4)

200

Find the coordinates of the point P that divides the segment joining (-3, 4) and (5, -2) in the ratio 3:2.

(1, 0)

300

Given points A(2, 4) and B(6, 10), find the point P that divides the line segment AB in a ratio of 3:5.

(4.5, 7.75)

400

Divide the line segment joining points (-4, 7) and (8, -3) in the ratio 2:3. Find the coordinates of the dividing point.

(0.8, 3)

500

Alice and Bob are sharing a 60-inch long piece of ribbon in the ratio 2:5. How many inches of ribbon will each person get?

Alice will get approximately 17.14 inches of ribbon, and Bob will get approximately 42.86 inches of ribbon.