Question

Find the value of k if PQ and RS are parallel, given P(1, 2), Q(4,5) and R(3, 4), S(8, k).

• A. 9
• B. 7
• C. -7
• D. -9

Answer 1

The correct option is A

9

Slope of PQ = $\frac{y_2–y_1}{x_2–x_1}$

=$\frac{5-2}{4-1}$ = $1$

Slope of RS = $\frac{y_2–y_1}{x_2–x_1}$

=$\frac{k-4}{8-3}$ = $\frac{k-4}{5}$

Since the lines are parallel, their slopes are equal.

$\frac{k-4}{5}=1$
$k-4=5$
$k=9$