Question 6

Explanation

From the diagram, the coordinates of the rhombus vertices are $P(0, 0)$, $Q(4, 3)$, $R(8, 0)$, and $S(4, -3)$.

Calculate the slope of line $PS$

With $P(0, 0)$ and $S(4, -3)$

Since the line we're looking for is perpendicular to $PS$, then

So the slope of the line passing through $Q$ and perpendicular to $PS$ is $m = \frac{4}{3}$.

For a line equation in the form $ax + by = c$, its slope is $m = -\frac{a}{b}$.

Find the answer option that has slope $\frac{4}{3}$.

Option $4x - 3y = 7$ has slope

Verify that this line passes through $Q(4, 3)$

Correct. Therefore, the equation of the line passing through $Q$ and perpendicular to $PS$ is $4x - 3y = 7$.