Question

you move up 3 units and down 7 units. you end at (5, -2). where did you start?

Explanation:

Step1: Analyze x-coordinate movement

The movement only affects the y-coordinate, so the starting x-coordinate equals the ending x-coordinate: $x_{\text{start}} = 5$

Step2: Define y-coordinate relationship

Let $y_{\text{start}}$ be the starting y-value. The net movement is $+3 -7$. Set up the equation:
$y_{\text{start}} + 3 - 7 = -2$

Step3: Solve for starting y-coordinate

Simplify and solve:
$y_{\text{start}} - 4 = -2$
$y_{\text{start}} = -2 + 4 = 2$

Answer:

$(5, 2)$