13. Find the coordinates of the point Q on the xaxiswhich lies on the

1.	13. Find the coordinates of the point Q on the xaxiswhich lies on the perpendicular bisector of theline segment joining the points A (-5, -2) andB (4,-2). Name the type of triangle formed by thepoints Q, A and B.
Answer» Let A be the point on the x-axis so, let A=(a,0) , B=(-5,-2) and C=(4,-2) Now, let D be the mid point of BC According to ur question A lies on the perpendicular bisector of the line joining B(-5,-2) and C(4,-2)That means, AD is perpendicular to BC and also bisects BC which means the triangle is isocelous Thus, use AB = AC=> (a + 5)^2+ 4 = (a - 4)^2+ 4 => (a + 5)^2- (a - 4)^2=0 => (a + 5 + a - 4)(a + 5 - a +4) = 0 => (2a + 1)(9) = 0 => a = -1/2

13. Find the coordinates of the point Q on the xaxiswhich lies on the perpendicular bisector of theline segment joining the points A (-5, -2) andB (4,-2). Name the type of triangle formed by thepoints Q, A and B.

Answer»

Let A be the point on the x-axis

so, let A=(a,0) , B=(-5,-2) and C=(4,-2)

Now, let D be the mid point of BC

According to ur question

A lies on the perpendicular bisector of the line joining B(-5,-2) and C(4,-2)That means, AD is perpendicular to BC and also bisects BC

which means the triangle is isocelous

Thus, use AB = AC=> (a + 5)^2+ 4 = (a - 4)^2+ 4

=> (a + 5)^2- (a - 4)^2=0

=> (a + 5 + a - 4)(a + 5 - a +4) = 0

=> (2a + 1)(9) = 0

=> a = -1/2