Question

c) Area of triangle formed by points A (1, 2), B (-1, 3) and C (4, k) is 8 square units then value of k is ?

Answer 1

Area of triangle

= √x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)

Here,

• x1 = 1
• x2 = -1
• x3 = 4
• y1 = 2
• y2 = 3
• y3 = k

To find :-

Value of k

Substituting values in formula,

√1(3 - k) + (-1)(k - (-2) + 4(2 - 3) = 8

√1(3 - k) - 1(k + 2) +4(-1) = 8

√3 - k - k - 2 - 4 = 8

√3 - 2 - 4 - 2k = 8

√- 3 - 2k = 8

- 3 - 2k = 64

- 2k = 64 + 3

- 2k = 67

k = -67/2

•°• Value of k is -67/2

Answer 2

SOLUTION :-

•We know that,

☞Area of triangle = √x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)

☞Where, x1 = 1 , x2 = -1 , x3 = , y1 = 2 , y2 = 3 , y3 = k.

☞Put the values in formula, we get

=> √1(3 - k) + (-1)(k - (-2) + 4(2 - 3) = 8

=> √1(3 - k) - 1(k + 2) +4(-1) = 8

=> √3 - k - k - 2 - 4 = 8

=> √3 - 2 - 4 - 2k = 8

=> √- 3 - 2k = 8

=> (√ -3 - 2k)² = (8)² ( Square on both sides. )

=> - 3 - 2k = 64

=> - 2k = 64 + 3

=> - 2k = 67

=> k = -67/2

Therefore, the value of k is -67/2 .