Question

1. find the scale factor that was used in the dilation shown.
2. if abc is translated 3 units up and then reflected over the x - axis, which describes the location of b?

a. (-3,-4)
b. (3,-4)
c. (3,4)
d. (4,3)

Explanation:

Question 17

Step1: Select corresponding sides

Let's take side \(RT\) and \(R'T'\).
The length of \(RT\): \(RT = 5 - 2=3\) (using the \(x -\)coordinates of \(R(2,2)\) and \(T(5,2)\)).
The length of \(R'T'\): \(R'T'=9 - 3 = 6\) (using the \(x -\)coordinates of \(R'(3,3)\) and \(T'(9,3)\)).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of image segment}}{\text{length of pre - image segment}}\).
\(k=\frac{R'T'}{RT}\)
Substitute \(R'T' = 6\) and \(RT = 3\) into the formula: \(k=\frac{6}{3}=2\)

Step1: Translation

The rule for a translation \(3\) units up is \((x,y)\to(x,y + 3)\).
For point \(B(-3,1)\), after translation \(B'\) has coordinates \((-3,1 + 3)=(-3,4)\).

Step2: Reflection over the \(x -\)axis

The rule for a reflection over the \(x -\)axis is \((x,y)\to(x,-y)\).
For point \(B'(-3,4)\), after reflection \(B''\) has coordinates \((-3,-4)\)

Answer:

\(2\)

Question 18

Assume \(B\) has coordinates \((- 3,1)\) (from the coordinate system in the problem).