# NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 5

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1. Find the area of the triangle formed by the lines .

The equations of the given lines are

………………………… eq (1)

……………………….. eq (2)

……………………..… eq (3)

The point of intersection of lines eq (1) and (2) is given by

The point of intersection of lines eq (2) and (3) is given by

The point of intersection of lines eq (3) and (1) is given by

So, the vertices of the triangle formed by the three given lines are .

We know that the area of a triangle whose vertices are is

So, area of the triangle formed by the three given lines

square units

square units

square units.

2. Find the value of p so that the three lines may intersect at one point.

The equations of the given lines are

………………………. eq (1)

…………………….. eq (2)

…………………….… eq (3)

On solving equations (1) and (3), we obtain

Since these three lines may intersect at one point, the point of intersection of lines (1) and (3) will also satisfy line (2).

The required value of p is .