Find the Midpoint or Missing Endpoint - and some review!

On a map, Julie’s house is located at (−2, 5) and Jimmy’s house is at (6, −3). What is the point halfway between Julie’s house and Jimmy’s house?

Answer explanation

On a map, Julie’s house is located at (−2, 5) and Jimmy’s house is at (6, −3). What is the point halfway between Julie’s house and Jimmy’s house?

Using the midpoint formula, we would

Find x by adding our two x's and dividing by 2 : (-2+6)/2 = 2

Find y by adding our two y's and dividing by 2: (5+ -3)/2 = 1

Then put them together into the coordinates (2,1) and graph on the x,y plane. Remember the x coordinate tells you how far left or right to place your point, and y tells you how far up or down to place it.

Tags

CCSS.HSG.GPE.B.6

On a map’s coordinate grid, Walt City is located at (−2, −3) and Koshville is located at (4, 9). If a train is travelling from Walt City to Koshville, at what point will it be exactly half way to it's destination?

Answer explanation

On a map’s coordinate grid, Walt City is located at (−2, −3) and Koshville is located at (4, 9). If a train is travelling from Walt City to Koshville, at what point will it be exactly half way to it's destination?

Using the midpoint formula, we would

Find x by adding our two x's and dividing by 2 : (-2+4)/2 = 1

Find y by adding our two y's and dividing by 2: (-3+ 9)/2 = 3

Then put them together into the coordinates (1,3) and graph on the x,y plane. Remember the x coordinate tells you how far left or right to place your point, and y tells you how far up or down to place it.

Tags

CCSS.HSG.GPE.B.6

Coach Alvarado drew his football team’s next play on the coordinate grid. He placed Kaleem at (10, 3). He will be passing the ball to Jeremy at (−6, 3). At what point will the ball be the same distance from Kaleem as it is from Jeremy?

Answer explanation

Coach Alvarado drew his football team’s next play on the coordinate grid. He placed Kaleem at (10, 3). He will be passing the ball to Jeremy at (−6, 3). At what point will the ball be the same distance from Kaleem as it is from Jeremy?

Using the midpoint formula, we would

Find x by adding our two x's and dividing by 2 : (10+ -6)/2 = 2

Find y by adding our two y's and dividing by 2: (3+3)/2 = 3

Then put them together into the coordinates (2,3) and graph on the x,y plane. Remember the x coordinate tells you how far left or right to place your point, and y tells you how far up or down to place it.

Tags

CCSS.8.G.A.2

The midpoint of segment 𝑋𝑌 is point 𝑀(−2, 3). If the coordinates of X are (4, −3), what are the coordinates of Y?

Answer explanation

The midpoint of segment 𝑋𝑌 is point 𝑀(−2, 3). If the coordinates of X are (4, −3), what are the coordinates of Y?

Since this problem gives us the midpoint and asks us to find the missing endpoint, we are going to first:

Double the midpoint - 2(-2,3) = (-4, 6)

Then subtract the x and y of the endpoint we know to find the endpoint we are missing.

-4 -4 = -8

6 - (-3) = 9

So our missing endpoint is (-8,9).

I also included a screenshot of how to easily do this process in Desmos.

Tags

CCSS.HSG.GPE.B.6

The midpoint of segment RS is point 𝑀( 2, 5). If the coordinated of 𝑅 are (−3, −6), what are the coordinates of 𝑆?

• ( - 0.5, - 0.5)

• ( 3.5, -4.5)

• ( 7, 16)

• 12.08

Answer explanation

The midpoint of segment RS is point 𝑀( 2, 5). If the coordinated of 𝑅 are (−3, −6), what are the coordinates of 𝑆?

Since this problem gives us the midpoint and asks us to find the missing endpoint, we are going to first:

Double the midpoint: 2( 2, 5) = ( 4, 10)

Then subtract the x and y of the endpoint we know to find the endpoint we are missing.

4 - (-3) = 7

10 - (-6) = 16

So our missing endpoint is ( 7, 16).

I also included a screenshot of how to easily do this process in Desmos.

Tags

CCSS.HSG.GPE.B.6

A line has one endpoint of (-3, 7) and a midpoint of (5, 2). What is the other endpoint?

• (-11, 12)

• (13, -3)

• ( 2, 3.5)

• 9.43

Answer explanation

A line has one endpoint of (-3, 7) and a midpoint of (5, 2). What is the other endpoint?

Since this problem gives us the midpoint and asks us to find the missing endpoint, we are going to first:

Double the midpoint: 2(5, 2) = (10, 4)

Then subtract the x and y of the endpoint we know to find the endpoint we are missing.

10 - (-3) = 13

4 - 7 = -3

So our missing endpoint is (13, -3).

I also included a screenshot of how to easily do this process in Desmos. You may notice I used A and B for the endpoints - I could have chosen any letters and this would work.

Tags

CCSS.HSG.GPE.B.6

What is the midpoint between ( 10, -7) and ( -5, 14)?

• (0, 3.5)
• (2.5, 3.5)
• (5, 3.5)
• (-2.5, 3.5)

Answer explanation

What is the midpoint between ( 10, -7) and ( -5, 14)?

Use the midpoint formula to solve. Remember to use the x's from each coordinate pair to find the new x and the y's from each coordinate pair to find the new y.

Tags

CCSS.HSG.GPE.B.6

Which of the following shows how you could solve for the midpoint between ( 5, 6) and (-4, -3)?

• 
• 
• 
• 

Answer explanation

The correct answer is the only one that shows the two x values being added and then divided by two to find x and the two y values being added and divided by 2 to find y. Look carefully at your formula and determine x1 y1 x2 and y2

Tags

CCSS.HSG.GPE.B.6

Find the midpoint of the segment on the graph. (Hover over picture to expand)

• (2,3)

• (-1,2)

• (5,-3)

• (3,2)

Answer explanation

The points on the graph are (1,5) and (3,1). Using that information, we follow the midpoint formula.

Tags

CCSS.HSG.GPE.B.6

Find the midpoint of point J and K

• (-3,3)
• (1,3)
• (-1,3)
• (2, 2.5)

Answer explanation

J is located at ( -5, 4) and K is located at ( 3, 2).

I find the midpoint by using those values in the midpoint formula.

Tags

CCSS.HSG.GPE.B.6