Question

A triangle with two vertices located at (5, −8) and (5, 4) has an area of 48 square units. Determine one possible location of the other vertex.

Answer 1

Answer:x=1.5

Step-by-step explanation:

Given

Two points co-ordinates are given

A=(5,-8)

B=(5,4)

let other point be C =(x,y)

Area of triangle is given by

$A=\begin{vmatrix}5& -8&1\\5& 4&1\\x& y&1\end{vmatrix}$

$A=5\left ( 4-y\right )+8\left ( 5-x\right )+1\left ( 5y-4x\right )$

A=20-5y+40-8x+5y-4x

A=60-8x

and A=48 square unit

48=60-8x

x=1.5

As area is independent of y therefore at x=1.5 any value of y will give area of 48 square unit