Question

determine if the point (-4,3),(0,3) And (2,3) are collinear​

Answer 1

Step-by-step explanation:

(x1,y1)=(-4,3)

(x2,y2)=(0,3)

(x3,y3)=(2,3)

1/2{(x2(y3-y1)+x3(y1-y2)+ x1(y2-y3)

1/2{0(3-3)+2(3-3)-4(3-3)}

1/2{0+0+0}

0

given points are collinear

Answer 2

Step-by-step explanation:

Given:(-4,3),(0,3) and (2,3)

To find: Determine whether the points are collinear or not.

Solution:

We know that collinear means lies on a straight line.

If three points lies on a straight line,they will never form a triangle.

Thus,we can say area formed by these points will be zero.

Area of triangle: A(x1,y1),B(x2,y2) and C(x3,y3)

$\boxed{\bold{\green{ar(\triangle \:ABC) = \frac{1}{2} \bigg|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \bigg| }}}$

Let points

A (-4,3), B(0,3) And C(2,3)

put these values in the formula

$ar( \triangle \: ABC)= \frac{1}{2} \bigg| - 4(3- 3) + 0(3 - 3) + 2(3 - 3) \bigg| \\ \\ ar( \triangle \: ABC)= \frac{1}{2} \bigg| - 4(0) + 0(0) + 2(0) \bigg| \\ \\ ar( \triangle \: ABC)= \frac{1}{2} \times 0 \\ \\ ar( \triangle \: ABC)= 0$

Thus,

All three points are collinear.

Hope it helps you.

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