Question

The line joining the points $(8,2),(-5,3)$ is neither parallel nor perpendicular to the line passing through points $(16,6)$ and $(3,15)$.

• A. False
• B. True

Answer 1

The correct option is B

True

We know that, slope(m) of the line formed by joining the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

Consider points $A(8,2)andB(-5,3)$.

Then, slope of $AB=\frac{3-2}{-5-8}=\frac{-1}{13}=m_1\left(say\right)$

Now, consider points P(16,6) and Q(3,15).

Then, slope of PQ=$\frac{15-6}{3-16}=\frac{-9}{13}=m_2\left(say\right)$

We see that $m_1\ne m_2$ and hence AB and PQ are not parallel.

Also, $m_1\times m_2\ne -1$ and hence AB and PQ are not perpendicular to each other.

Therefore, the given statement is true.