Question

If the points (x, y), (-5,-2) and (3,-5) are
collinear, prove that 3x + 8y +31=0.
​

Answer 1

Answer:

3*-5+8*-2+31=0

-15+(-16)+31=0

-31+31=0

2nd equation

3*3+8*-5+31=0

9+(-40)=0

Hence proved the values are not collinear

Step-by-step explanation:

replace x and y values

Answer 2

Given :-

( x ,y) , ( -5 , -2) and ( 3 , -5)

To prove :-

3x + 8y + 31 = 0

Proof :-

Collinear points :- The points which lie in a line segment such that the distance between the points are equal is known as collinear points.

$x_1 = x , x_2 = -5 , x_3 = 3\\</p><p>y_1 = y , y_2 = -2 , y_3 = -5$

Condition for collinearity :-

$\dfrac{1}{2}[ x_1 (y_2 - y_3 ) + x_2 ( y_3 - y_1 ) + x_3 ( y_1 - y_2 )] = 0$

Put the given value ,

→$[ x { -2 - (-5)}] + (-5 ) [ -5 -y ] + 3 [ y - (-2)] = 0$

→$[ x ( -2 + 5)] -5 ( -5 -y ) + 3 ( y +2) = 0$

→$x \times 3 + 25 +5y +3y +6 = 0$

→$3x + 25 + 8y + 6 = 0$

→$3x + 8y + 31 = 0$

hence,

R.H.S = L.H.S proved..