Question

The midpoint of the points on x + y = 4 and 4x + 3y - 10 = 0 which are at a distance of 4 units is the point of intersection of the two lines given.

• A. True
• B. False

Answer 1

The correct option is A

True

We draw perpendicularfrom $L_2$ to meet $L_1$ at different points. Some of these perpendicular are going to be 1 unit. As we can see the length of the perpendicular is zero at the point of contact and it increases as we move on either side. We can see that there will be exactly two points which are at unit distance from $L_2$. Let those points be $P(x_1,y_1)andQ(x_2,y_2)$.

The two triangle formed are congruent triangles.
$\Rightarrow$ OP=OQ
$\Rightarrow$ O is the midpoint of P and Q. To find the midpoint, we just have to find the point of intersection.