Question

For what value of x are the points a(-3,12),b(7,6),c(x,9) collinear

Answer 1

Answer:

The value of x=2

Step-by-step explanation:

Given : The points a(-3,12),b(7,6),c(x,9) are collinear

To find : The value of x

Solution :

If there are three points which lie on the same line i.e they are collinear then the area of the triangle formed by those three points is zero.

The area of a triangle given the coordinates of the three points can be found by using the below formula:

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

where,

$(x_1,y_1)= (-3,12)$

$(x_2,y_2)= (7,6)$

$(x_3,y_3)= (x,9)$

represents the three points of the triangle.

Substitute, the value in the formula,

$A= \frac{1}{2}[-3(6-9) + 7(9-12) + x(12-6)]$

$0= \frac{1}{2}[-3(-3) + 7(-3) + x(6)]$

$0= \frac{1}{2}[9 -21 +6x]$

$0=-12+6x$

$x=\frac{12}{6}$

$x=2$

Therefore, The value of x=2.

Answer 2

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