plot each point and form the triangle ABC.Verify that the triangle is a right triangle. Find its area.

Question

A =(-2,5); B = (1, 3), C = (-1, 0)

Answer 1

Step 1:

The points are , and .

Graph:

Plot the points  , and  .

Connect the plotted points.

Step 2:

The distance between and is .

The distance between and is

The distance between and is

The distance between and is

 

Pythagoras theorem:

For right angled triangle, square of hypotenuse is equal to sum of squares of other two sides.

As Pythagoras theorem is satisfied, ΔABC is right angled triangle.

Step 3:

The area of a triangle is .

Where and .

Solution:

ΔABC is right angled triangle.

Area of ΔABC is 6.5 sq-units.