Chapter 4, Problem 3SAP

To determine

To find: coordinates of point C.

Answer to Problem 3SAP

C. $\left(d-a,b\right)$

Explanation of Solution

Given information: ABCD is a parallelogram.

  

A. $\left(x,y\right)$

B. $\left(d+a,y\right)$

C. $\left(d-a,b\right)$

D. $\left(d+x,b\right)$

E. $\left(d+a,b\right)$

Calculation:

Distance between A and D = | d − 0| = d

Since the opposite sides of a parallelogram are equal, the distance between B and C is also d .

Also, the y -coordinates of A and D are equal, the side AD is parallel to the x -axis.

And, since ABCD is a parallelogram, BC is also parallel to the x -axis.

So the y -coordinates of B and C are also equal.

Thus, the x -coordinate of C = d − a .

Hence, the coordinates of C are $\left(d-a,b\right)$ .

So the correct answer is C.