Question

which of the following steps were applied to △abc obtain △abc?
a. shifted 4 units right and 3 units up
b. shifted 2 units right and 3 units up
c. shifted 3 units right and 2 units up
d. shifted 3 units right and 3 units up

Explanation:

Step1: Analyze horizontal shift

Take a point (e.g., point A). If original \(x -\) coordinate is \(x_1\) and new \(x -\) coordinate is \(x_2\). Count the number of units between them on the \(x -\) axis. For example, if \(x_1 = 1\) and \(x_2=5\), the shift is \(x_2 - x_1=4\) units to the right.

Step2: Analyze vertical shift

Take the same point. If original \(y -\) coordinate is \(y_1\) and new \(y -\) coordinate is \(y_2\). Count the number of units between them on the \(y -\) axis. For example, if \(y_1 = 5\) and \(y_2 = 8\), the shift is \(y_2 - y_1=3\) units up.

Since for all corresponding points (A - A', B - B', C - C') the horizontal shift is 4 units right and vertical shift is 3 units up, the transformation is shifted 4 units right and 3 units up.

Answer:

A. Shifted 4 units right and 3 units up