QuestionFind point $A$ if midpoint $M(-1,2)$ of line segment $\overline{AB}$ and $B(3,-5)$ .

Studdy Solution

STEP 1

Assumptions1. Point $M(-1,)$ is the midpoint of the line segment $\overline{A B}$ . . The coordinates of point $B$ are $(3,-5)$ .
3. We need to find the coordinates of point $A$ .

STEP 2

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

STEP 3

We know the coordinates of $M$ and $B$ , so we can set up the following equations to solve for the coordinates of $A$ $-1 = \frac{x1 +3}{2}$ $2 = \frac{y1 -5}{2}$

STEP 4

To solve for $x1$ , multiply both sides of the first equation by2 and subtract3 $-1 \times2 = x1 +3$ $x1 = -2 -3$

STEP 5

Calculate the value of $x1$ $x1 = -2 -3 = -5$

STEP 6

To solve for $y1$ , multiply both sides of the second equation by2 and add5 $2 \times2 = y1 -5$ $y1 =4 +5$

STEP 7

Calculate the value of $y1$ $y1 =4 +5 =9$

STEP 8

The coordinates of point $A$ are $(x1, y1)$ , so $A = (-5,)$ The coordinates of point $A$ are $(-5,)$ .

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