#### Question

If sum of the perpendicular distances of a variable point P (*x*,* y*) from the lines *x* + *y* – 5 = 0 and 3*x* – 2*y*+ 7 = 0 is always 10. Show that P must move on a line.

#### Solution

The equations of the given lines are

*x* + *y* – 5 = 0 … (1)

3*x* – 2*y* + 7 = 0 … (2)

The perpendicular distances of P (*x*, *y*) from lines (1) and (2) are respectively given by

Is there an error in this question or solution?

Solution If Sum of the Perpendicular Distances of a Variable Point P (X, Y) from the Lines X + Y – 5 = 0 and 3x – 2y + 7 = 0 is Always 10. Show that P Must Move on a Line. Concept: Distance of a Point from a Line.