Question

The points A(2,9),B(k,5)and C(5,5) are the vertices of triangle ABC right angle triangle at B. Find the value of K. Hence area of triangle.

Answer 1

Answer:

According to Pythagoras theorem,

{(K-2)^2+(5-9)^2}+{(k-5)^2+(5-5)^2}={(5-2)^2÷(5-9)^2}

K^2-7k+10 will be the equation after solving above equation

Then k-5 & k-2 will be the factors.

But k=2

When k=5 the points B &C will coincide.so k=2.

Area= 1/2xABxBC

Area= 1/2×4×3=6.

Area of triangle is 6