QuestionFind the coordinates of point $B$ if the midpoint $M(-2,-2)$ and point $A(-3,-6)$ are given.

Studdy Solution

STEP 1

Assumptions1. The midpoint of a line segment $\overline{\mathrm{AB}}$ is given by $M(-,-)$ . . The coordinates of point $A$ are $(-3,-6)$ .
3. We are to find the coordinates of point $B$ .

STEP 2

The formula for the midpoint of a line segment with endpoints $(x1, y1)$ and $(x2, y2)$ is given by $M = \left(\frac{x1+x2}{2}, \frac{y1+y2}{2}\right)$

STEP 3

We can set up two equations using the given midpoint and one endpoint to solve for the coordinates of the other endpoint. The equations are $-2 = \frac{-3+x_B}{2}$ $-2 = \frac{-6+y_B}{2}$

STEP 4

We solve the first equation for $x_B$ $-2 = \frac{-3+x_B}{2}$ Multiply both sides by2 $-4 = -3 + x_B$ Then add3 to both sides $-1 = x_B$

STEP 5

We solve the second equation for $y_B$ $-2 = \frac{-+y_B}{2}$ Multiply both sides by2 $-4 = - + y_B$ Then add to both sides $2 = y_B$ So, the coordinates of point B are $(-1,2)$ .

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