Chapter 11, Problem 16RP

To determine

To calculate:Thecoordinates of point B such that triangle ABD and triangle ACD will have same area .

Answer to Problem 16RP

The coordinates of point Bare $\left(-2,0\right)$ .

Explanation of Solution

Given information:

ΔABD = ΔACD

The coordinates of point Aare $\left(0,9\right)$ .

The coordinates of point C are $\left(14,0\right)$ .

The coordinates of point Dare $\left(6,0\right)$ .

Calculation:

  

It is given that, ΔABD = ΔACD

Both triangles have the same height, so their bases must be equal for their areas to be equal.

The base of ΔACD is 8.

Subtracting 8 from 6 gives the coordinates for B.

Point B lies on negative x −axis. The y coordinate of point B is 0.

The x coordinate is obtained by subtracting 8 from 6.

The coordinates of point Bare $\left(-2,0\right)$ .