Question

geometry
midterm exam
part 2:
name
date
period
multiple choice
identify the choice that best completes the statement or answers the questions. write all answer choices on the line provided.
transformation: translation

1. express the transformation of the image in word form.

(x, y) → (x + 3, y - 2)
a. 3 units left
2 units up
c. 3 units up
2 units left
b. 3 units right
2 units down
d. 3 units up
2 units down
transformation: translation

1. express the transformation of the image in arrow notation form.

13 units left and 7 units up
a. (x, y) → (x - 13, y + 7)
d. (x, y) → (x - 7, y + 13)
b. (x, y) → (x - 13, y - 7)
e. (x, y) → (x + 13, y - 7)
c. (x, y) → (x - 7, y + 13)

Explanation:

Question 1

Step1: Analyze x - coordinate change

In the transformation \((x,y)\to(x + 3,y - 2)\), the \(x\) - coordinate changes from \(x\) to \(x+3\). When the \(x\) - coordinate increases by a positive number, the point moves to the right. So, the horizontal movement is 3 units to the right.

Step2: Analyze y - coordinate change

The \(y\) - coordinate changes from \(y\) to \(y - 2\). When the \(y\) - coordinate decreases by a positive number, the point moves down. So, the vertical movement is 2 units down.

Step1: Analyze horizontal (x - coordinate) transformation

For a horizontal transformation, moving left means a decrease in the \(x\) - coordinate. If we move 13 units left, the change in the \(x\) - coordinate is \(x\to x-13\) (because subtracting a positive number from \(x\) moves the point to the left on the coordinate plane).

Step2: Analyze vertical (y - coordinate) transformation

For a vertical transformation, moving up means an increase in the \(y\) - coordinate. If we move 7 units up, the change in the \(y\) - coordinate is \(y\to y + 7\) (because adding a positive number to \(y\) moves the point up on the coordinate plane).

Step3: Write the arrow notation

Combining the horizontal and vertical transformations, the arrow notation for the transformation "13 units left and 7 units up" is \((x,y)\to(x - 13,y + 7)\).

Answer:

B. 3 units right
2 units down

Question 2