# Coordinate Geometry Short Questions (Question 3, 4 & 5)

Question 3:
The equation of the straight lines CD and EF are 5x + y – 4 = 0 and $\frac{x}{7}-\frac{y}{h}=1$ . If CD and EF are parallel, find the value of h.

Solution:
Two parallel lines have same gradient.
5x + y – 4 = 0
y = –5x + 4, mCD = –5

For the straight line EF,
$\begin{array}{l}\frac{x}{7}-\frac{y}{h}=1\\ {m}_{EF}=-\left(\frac{y\text{-intercept}}{x\text{-intercept}}\right)=-\left(\frac{-h}{7}\right)=\frac{h}{7}\\ {m}_{CD}={m}_{EF}\\ -5=\frac{h}{7}\\ h=-35\end{array}$

Question 4:
The straight line $\frac{x}{5}+\frac{y}{p}=1$ has a y-intercept of 3 and is parallel to the straight line y + qx = 0. Determine the value of p and of q.

Solution:

Question 5:
The equations of two straight lines  $\frac{y}{7}+\frac{x}{4}=1$ and 7y = 4x + 21. Determine whether the lines are perpendicular to each other.

Solution:

Hence, the two straight lines are perpendicular to each other.