Question

On a coordinate grid, JK has endpoint J at (15, −2), the midpoint of is M (1, −7). What is the length of JK?

Answer 1

Step 1: Determine the coordinates of the endpoint K
Step 2: Use Pythagorean Theorem to determine the length `|JK|`

Step 1
If M is the mid point of JK then the changes in `x` and `y` are the same from J to M and from M to K
`Delta x(J:M) = 1-15 = -14`
`Delta y(J:M) = -7-(-2) = -5`

The coordinates of K are
`M+(-14,-5) = (1,-7)+(-14,-5) = (-13,-12)`

Step 2:
`| JK | = sqrt((Delta x(J:K))^ + (Delta y(J:K))^2)`
based on the Pythagorean Theorem

`|JK| = sqrt( (-13-15)^2 + (-12-(-2))^2)`

`=sqrt(884)`

`=2sqrt(441)`