Question

A triangle with vertices A (1,k) and B (4,-3) and C (-7,9) and area =15

Answer 1

If (x1, y1), (x2, y2) and (x3, y3) are the vertices of a triangle then its area is given by   1 2 [x1(y2 - y3) + x2( y3 - y1)+ x3(y1 - y2)] square units. Given the vertices of a triangle are (1,-3),(4,k) and (-9,7) and its area is 15 sq .units. ⇒ 15 =   1 2 [1(k - 7) + 4( 7 + 3) + (-9)(-3 - k)] 30 = k - 7 + 40 + 27 + 9k 10k + 60 = 30 10k = -30 ∴ k = -3.

Answer 2

k=-3

By using the area formula.