Question

parallelograms ksvt and lnpr are shown on the coordinate plane.
a. complete the algebraic description of the transformation that maps parallelogram ksvt to lnpr. (x, y) → ( , )
b. complete the algebraic description of the transformation that maps parallelogram lnpr to ksvt. (x, y) → ( , )
c. what do you notice about the algebraic descriptions for these two translations?

Explanation:

Step1: Find the horizontal and vertical shift from KSVT to LNPR

Pick a vertex, say K(-7, 5). Its corresponding vertex in LNPR is L(0, 1). The change in x - coordinate is \(0-(-7)=7\) and the change in y - coordinate is \(1 - 5=-4\).

Step2: Write the transformation rule from KSVT to LNPR

The transformation rule \((x,y)\to(x + 7,y-4)\) maps parallelogram KSVT to LNPR.

Step3: Find the reverse transformation from LNPR to KSVT

The reverse of adding 7 to x and subtracting 4 from y is subtracting 7 from x and adding 4 to y. So the transformation rule \((x,y)\to(x - 7,y + 4)\) maps parallelogram LNPR to KSVT.

Step4: Analyze the relationship between the two transformation rules

The transformation from KSVT to LNPR is \((x,y)\to(x + 7,y-4)\) and from LNPR to KSVT is \((x,y)\to(x - 7,y + 4)\). The x - and y - values of the translation vectors are additive inverses of each other.

Answer:

a. \((x,y)\to(x + 7,y-4)\)
b. \((x,y)\to(x - 7,y + 4)\)
c. The x - and y - components of the translation vectors for the two translations are additive inverses of each other.