Question

Rectangle ABCD is on the coordinate plane. The equation of line AB is y=(2/3)x+4. What is the slope of line AD? Explain your reasoning.Pleas help me with this

Answer 1

Since ABCD is a rectangle, the sides AB and AD are perpendicular.

The slopes of perpendicular segments or lines have the following relation:

$m_2=-\frac{1}{m_1}$

The equation for the line AB is in the slope-intercept form: y = mx + b.

Therefore we can identify its slope: m1 = 2/3.

Now, calculating the slope m2 of line AD, we have:

$m_2=-\frac{1}{\frac{2}{3}}=-\frac{3}{2}$

Therefore the slope of line AD is equal to -3/2.