# Find the Value of K So that the Area of the Triangle with Vertices a (K+1, 1), B(4, -3) and C(7, -k) is 6 Square Units - Mathematics

Find the value of k so that the area of the triangle with vertices A (k+1, 1), B(4, -3) and C(7, -k) is 6 square units

#### Solution

"Let" A(x_1,y_1) = A(k+1,1) , B(x_2,y_2)= B (4,-3) and C(x_3,y_3) = C(7,-k) now

"Area "(Δ ABC) = 1/2 [x_1 (y_2-y_3) + x_2 (y_3-y_1) +x_3(y_1-y_2)}

⇒ 6=1/2 [(k+1) (-3+k)+4(-k-1) +7(1+3)]

⇒6=1/2[k^2 -2k-3-4k-4+28]

⇒ k^2-6k+9=0

⇒(k-3)^2 = 0⇒k=3

Hence , k=3

Concept: Area of a Triangle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 11