Question

4
use the drawing tool(s) to form the correct answer on the provided graph.
using the information provided on the graph, draw the line that is perpendicular to line ab and passes through point p.
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Explanation:

Step1: Find slope of line AB

First, identify points: $A(0, 3)$, $B(-2, 0)$.
Slope formula: $m_{AB}=\frac{y_2-y_1}{x_2-x_1}=\frac{0-3}{-2-0}=\frac{3}{2}$

Step2: Find perpendicular slope

Perpendicular slope is negative reciprocal:
$m_{\perp}=-\frac{1}{m_{AB}}=-\frac{2}{3}$

Step3: Identify point P

From graph, $P(8, -7)$

Step4: Write perpendicular line equation

Use point-slope form $y-y_1=m(x-x_1)$:
$y-(-7)=-\frac{2}{3}(x-8)$
Simplify: $y+7=-\frac{2}{3}x+\frac{16}{3}$
$y=-\frac{2}{3}x+\frac{16}{3}-\frac{21}{3}$
$y=-\frac{2}{3}x-\frac{5}{3}$

Step5: Plot the line

Find a second point: when $x=2$, $y=-\frac{2}{3}(2)-\frac{5}{3}=-\frac{4}{3}-\frac{5}{3}=-3$. So plot $(2, -3)$ and connect to $P(8, -7)$ to draw the perpendicular line.

Answer:

The line with equation $y=-\frac{2}{3}x-\frac{5}{3}$, passing through $P(8, -7)$ and $(2, -3)$, is the perpendicular line to AB. To complete the task, draw this line on the provided graph using the line tool, connecting these two points.