IDENTIFY THE TYPE OF TRIANGLE FROM THE GIVEN COORDINATES

Problem 1 :

Name the type of triangle formed by the points A(-5, 6), B(-4, -2) and C(7, 5).

Solution:

The three vertices of the triangle are A(-5, 6), B(-4, -2) and (7, 5)

By distance formula,

By distance formula,

By distance formula,

Length of all sides of the triangle are different.

So, ABC is a scalene triangle.

Problem 2 :

Find the coordinates of the point Q on the x axis which lies on the perpendicular bisector of the line segment joining the points A(-5, -2) and B(4, -2). Name the type of triangle formed by the points Q, A and B.

Solution:

Let the points as Q(x, y) = (x, 0) which is equidistant from A(-5, -2) and B(4, -2).

The distance between two points P(x₁, y₁) and Q(x₂, y₂) is 

Take square on both sides,

(-5 - x)² + 4 = (4 - x)² + 4

(-5 - x)² = (4 - x)²

25 + 10x + x² = 16 - 8x + x²

18x + 9 = 0

18x = -9

x = -9/18

x = -1/2

Therefore, the point Q is (-1/2, 0).

AQ = BQ

So, ΔQAB is an isosceles triangle.