Question

If P(2, 4), Q(3, 6), R(8, 1) and S(10, k) are vertices of a parallelogram .Then find the value of k.

Answer 1

Given: P(2, 4), Q(3, 6), R(8, 1) and S(10, k )

Now, slope of a line = $\frac{y_2-y_1}{x_2-x_1}=\frac{y_1-y_2}{x_1-x_2}$

Slope of line PQ =$\frac{6-4}{3-2}=\frac{2}{1}=2$

Slope of line RS= $\frac{k-1}{10-8}=\frac{k-1}{2}$

PQ is parallel to RS.
Then slope of line PQ = slope of line RS

$$\begin{gathered} \Rightarrow 2=\frac{k-1}{2} \\ \Rightarrow \frac{k-1}{2}=2 \\ \Rightarrow k-1=4 \\ \Rightarrow k=5 \end{gathered}$$