Chapter 11.1, Problem 13PSB

To determine

To find : The coordinates of point A

Answer to Problem 13PSB

The coordinates of point A are $(18,8)$

Explanation of Solution

Given information : The following information has been given

Area of rectangle RCTN is 6 times the area of rectangle AECT

Formula used : The area of any rectangle will be

  $A=(lengt{h}_1)(widt{h}_1)$

Thus, for rectangles with common width, the area is directly proportional to the length of the side

Calculation : We know that as the two rectangles share two common sides,

Measure of line NT will be six times the measure of AT

Hence, we divide the x coordinates $24$ to $\left(-12\right)$ into six parts.

Thus, we get the x coordinate of A as

  $A_x=24-\left(\frac{24-(-12)}{6}\right)=18$

Also, we know that

  $A_y=T_y=8$

Thus, the final coordinates are

  $A=(18,8)$