Question

Find the mid-point of the points on x + y = 4 which are at a unit distance from the line 4x + 3y - 10 = 0

• A. (-2, 6)
• B. (2, 2)
• C. (-7, 11)
• D. (1, 3)

Answer 1

The correct option is A

(-2, 6)

We draw perpendicular from $L_2$ to mmeet $L_1$ at different points. Some of these perpendicular are going to be 1 unit. As we can see the lenght of the perpendicular is zero at the point of contact and it increases as we move on either side. We can seethat 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.

O is the centre.