Question

The points A (4, -5), B (1, 1) and C (-2, y) are collinear with B lying

Answer 1

Answer:

y=-20/3

Step-by-step explanation:

area of triangle=0

4*(1-y)+1*(y+5)-2(-5-1)=0

4-4y+y+5+10+1=0

-3y+20=0

y=-20/3

Answer 2

Here,

• A(4, -5), B(1, 1), & C(-2, y)

To find : Value of y

As,

A, B, and C are collinear points, ar(∆ABC) is equal to zero.

$\small \rm ar(\triangle{ABC}) = \frac{1}{2} \bigg\{x_{\tiny{1}}(y_{\tiny{2}} - y_{\tiny{3}}) + x_{\tiny{2}}(y_{\tiny{3}} - y_{\tiny{1}}) +x_{\tiny{3}}(y_{\tiny{1}} - y_{\tiny{2}}) \bigg\} = 0$

$\tt\implies \frac{1}{2} \bigg\{4(1 - y) +1(y - \{ - 5 \}) + \{ - 2( - 5 - 1) \}\bigg\} = 0\\ \\ \small \tt\implies \frac{1}{2} \bigg\{4 - 4y + y + 5 + 10 + 1\bigg\} = 0 \\ \\ \tt\implies \frac{1}{2}\bigg\{20 - 3y\bigg\} = 0 \\ \\ \tt\implies \frac{20 - 3y}{2} = 0 \\ \tt\implies20 - 3y = 0 \\ \tt\implies \cancel - 3y = \cancel - 20 \\ \tt\implies y \: = \red{ \frac{20}{3} }$

Thus,

• Value of y is 20/3