Find the missing endpoint, Given the other endpoint and the midpoint.

Question

Find the coordinates of the missing endpoint Q if P(5, 2) is the midpoint of segment NQ and N(2, 0).

Answer 1

There are multiple ways to solve this type of problem, I'll show you the simplest way firstly you will need the midpoint formula:

The simplest way is to work in reverse. To find midpoint you add your points and divide by two, so to find an endpoint you only need to do the opposite, double the midpoint and subtract the endpoint:

x-value: 5(2) - 2 = 10 - 2 = 8

y-value: 2(2) - 0 = 4 - 0 = 4

So your other endpoint at Q would be (8, 4). Hope this helped!

Answer 2

Hi Audrey

Q(8, 4)

Find the coordinates of the missing endpoint Q if P(5, 2) is the midpoint of segment NQ and N(2, 0)

You can use the Midpoint formula directly to solve for the missing endpoint with the data given

Let the coordinates of

N(2, 0) the first endpoint = (x₁, y₁)

P(5, 2) the midpoint = (x, y)

Q the missing endpoint = (x₂, y₂)

Midpoint Formula

(x₁ + x₂/2, y₁ + y₂/2)

Where

(x₁ + x₂)/2 = x coordinate of the Midpoint

(y₁ + y₂)/2 = y coordinate of the Midpoint

Since you have coordinates for one endpoint and the midpoint you can plug them in and solve for the missing parts (x₂, y₂)

(2 + x₂)/2 = 5

Multiply both sides of the equation by 2

2 + x₂ = 10

Subtract 2 from both sides of the equation

x₂ = 8

Repeat the process for y₂ the y coordinate of the endpoint

(0 + y₂)/2 = 2

y₂ = 4

I hope you find this useful.

Answer 3

5 is 3 more than 2, for the x coordinate, so add 3 to 5 to get 8 for the x coordinate of Q

2 is 2 more than 0, for the y coordinate, so add 2 to 2 to get 4 as the y coordinate of Q

Q is (8,4)

or you could get the equation of the line through all three points

using the point slope formula. slope m = rise/run = 2/3 = (2-0)/(5-2)

then plug in one point & the slope into

y-h=m(x-k) where (k,h) = (2,0)

y-0 = (2/3)(x-2)

y= 2x/3 - 4/3

x changes from 2 to 5 from one end point to the midpoint, so it changes another 3 from the midpoint to the other end point, or 5+3 = 8 for the x coordinate

y=2(8)/3 - 4/3 = 16/3 - 4/3 = 12/3 = 4 for the y coordinate of the endpoint Q is (8,4)