Question

If a point a an endpoint of a AC has coordinates (8,4) and point B, the midpoint of AC has coordinates (-2,7) what is the X value of the coordinates of point C

Answer 1

The x-value of the coordinates of point C is -12.

Explanation:

Let be
`A = (8, 4)` and
`B = (-2, 7)`, which is midpoint of segment AC. The location of point C is obtained from the midpoint formula, that is:

`B = (1)/(2)\cdot A + (1)/(2)\cdot C`

`2\cdot B = A + C`

`C = 2\cdot B - A`

`C = 2\cdot (-2,7)-(8,4)`

`C = (-4,14)-(8,4)`

`C = (-4-8,14-4)`

`C = (-12,10)`

The x value is the first component of the ordered pair, that is:
`x = -12`. The x-value of the coordinates of point C is -12.