QuestionFind the coordinates of point $B$ if the midpoint $M(5,-3)$ and point $A(3,-8)$ are given.

Studdy Solution

STEP 1

Assumptions1. The midpoint of a line segment with endpoints $(x1, y1)$ and $(x, y)$ is given by $\left(\frac{x1+x}{}, \frac{y1+y}{}\right)$ . . The midpoint $M$ of $\overline{\mathrm{AB}}$ is given as $(5,-3)$ .
3. The coordinates of point $A$ are given as $(3,-8)$ .
4. We are asked to find the coordinates of point $B$ .

STEP 2

We can write down the formula for the midpoint of a line segment.
$M = \left(\frac{x1+x2}{2}, \frac{y1+y2}{2}\right)$

STEP 3

We know the coordinates of the midpoint $M$ and point $A$ , so we can substitute these into the formula to get two equations.
$5 = \frac{3 + x_B}{2}$ $-3 = \frac{-8 + y_B}{2}$

STEP 4

We can solve the first equation for $x_B$ by multiplying both sides by2 and then subtracting3.
$x_B =2 \cdot -3$

STEP 5

Calculate the $x$ -coordinate of point $B$ .
$x_B =2 \cdot5 -3 =7$

STEP 6

We can solve the second equation for $y_B$ by multiplying both sides by2 and then adding8.
$y_B =2 \cdot -3 +8$

STEP 7

Calculate the $y$ -coordinate of point $B$ .
$y_B =2 \cdot -3 + =2$ The coordinates of point $B$ are $(7,2)$ .

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