Question

If P(3,-5), Q(-2,k), R(1,4) are vertices of
triangle PQR and its area is 17/2 square
unit then find the value of k.​

Answer 1

Given,

Three vertices are = P(3,-5), Q(-2,k), R(1,4)

Area = 17/2 square unit

To find,

The value of k.

Solution,

We can easily solve this mathematical problem by the following mathematical process.

Let,

P = (3,-5) = X1,Y1

Q = (-2,k) = X2,Y2

R = (1,4) = X3,Y3

Area of the triangle :

= ½ × [X1 (Y2-Y3) + X2 (Y3-Y1) + X3 (Y1-Y2)]

= ½ × [3×(k-4) + (-2) × (4+5) + 1 × (-5-k)]

= ½ × [(3k-12)+(-18)+(-5-k)]

= ½ × (3k-12-18-5-k)

= ½ × (2k-35) square unit

According to the data mentioned in the question,

½ (2k-35) = 17/2

½ (2k-35) = 17 × ½

2k-35 = 17

2k = 17+35

2k = 52

k = 26

Hence, the value of k is 26