Question

The area of the triangle is 18 sq. units, whose vertices are (3, 4), (-3, -2) and (p, -1); then find the value of 'p'.​

Answer 1

Hope, it helps you.......

Answer 2

The value of p is either 4 or -8.

Step-by-step explanation:

The vertices of a triangle are (3, 4), (-3, -2) and (p, -1).

The area of a triangle is

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

Using the above formula the area of given triangle is

$A=\frac{1}{2}|3(-2-(-1))+(-3)(-1-4)+p(4-(-2))|$

$A=\frac{1}{2}|3(-1)+(-3)(-5)+p(6)|$

$A=\frac{1}{2}|-3+15+6p|$

$A=\frac{1}{2}|12+6p|$

It is given that area of the triangle is 18 sq. units.

$18=\frac{1}{2}|12+6p|$

Multiply both sides by 2.

$36=|12+6p|$

We know that |x|=|-x|=x, so we get

$\pm 36=12+6p$

$36=12+6p\Rightarrow 24=6p\Rightarrow p=4$

$-36=12+6p\Rightarrow -48=6p\Rightarrow p=-8$

Therefore, the value of p is either 4 or -8.

#Learn more

If the vertices of a triangle are (1,2),(4,-6)and(3,5) then find the area of triangle.

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