QuestionFind endpoint $Q$ if $M$ is the midpoint of $\overline{PQ}$ , with $P(-2,3)$ and $M(5,1)$ .

Studdy Solution

STEP 1

Assumptions1. $M$ is the midpoint of $\overline{ Q}$ . . The coordinates of point $$ are $(-,3)$.
3. The coordinates of point $M$ are $(5,1)$.
4. The coordinates of point $Q$ are unknown.

STEP 2

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

STEP 3

We can rearrange the midpoint formula to solve for $x2$ and $y2$ (the coordinates of point $Q$ ):
$x2 =2x_M - x1$ $y2 =2y_M - y1$

STEP 4

Substitute the given values into the equations from3 to find the $x$ -coordinate of point $Q$ $x2 =2() - (-2)$

STEP 5

Calculate the $x$ -coordinate of point $Q$ $x2 =2(5) - (-2) =10 +2 =12$

STEP 6

Substitute the given values into the equations from3 to find the $y$ -coordinate of point $Q$ $y2 =2(1) -3$

STEP 7

Calculate the $y$ -coordinate of point $Q$ $y2 =2(1) -3 =2 -3 = -1$ The coordinates of point $Q$ are $(12, -1)$ .

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