Question

plot each point and form the triangle ABC. Verify that the triangle ABC is a right triangle. Find its area. A= (-5, 10) B (2,7) C (-1,0)

Answer 1

Answer: The triangle is right angled triangle. and the area of the trianlge is 29 unit².

Explanation: The plot of the points A, B and C is attahced below.

In the triangle ABC, the three arms AB, BC and AC can be calculated using the formula for the distance between two points (x₁, y₁) and (x₂, y₂) as following.

--------------------------------------------- (1)

So, for AB, (x₁, y₁)=(-5, 10) and (x₂, y₂)=(2, 7). So,

    --------- (2)

For, BC, (x₁, y₁)=(2, 7) and (x₂, y₂)=(-1, 0). So,

------------- (3)

For, CA, (x₁, y₁)=(-1, 0) and (x₂, y₂)=(-5, 10). So,

----------- (4)

So, from eqn 2, 3 and 4. we get.

So, we see that,

Hence, the triangle, ABC is right angled triangle.

(AREA OF THE TRIANGLE)