Question

If m is the midpoint of a line XY, find the coordinates of x if m(-3, -1) and Y(-8, 6)

Answer 1

X(2, -8)

Given:

m(-3, -1), Y(-8, 6)

To find the coordinates of X, use the midpoint formula below:

`(x_(m.)y_m)\text{ = (}(x1+x2)/(2),\text{ }(y1+y2)/(2))`

Where,

(xm, ym) = (-3, -1)

(x2, y2) = (-8, 6)

Let the coordinates of x be (x1, y1)

Therefore, we have:

`\begin{gathered} x_m\text{ = }(x1+x2)/(2) \\ \text{Substitute values to solve for x}1 \\ -3\text{ =}(x1+(-8))/(2) \\ -6\text{ = x1 - 8} \\ x1\text{ = -6 + 8} \\ x1\text{ = 2} \end{gathered}`
`\begin{gathered} \text{For y1:} \\ y_m\text{ = }(y1+y2)/(2) \\ Substitute\text{ values in the equation to find y1:} \\ -1\text{ = }(y1+6)/(2) \\ 2(-1)\text{ = y1 + 6} \\ -2\text{ = y1 + 6} \\ y1\text{ = -6 - 2} \\ y1\text{ = -8} \end{gathered}`

The coordinates of X(x1, y1) = X(2, -8)