Question

10.4.2 quiz: transformations
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 3 units up
d. shifted 3 units right and 2 units up

Explanation:

Step1: Find coordinates of a point

Let's take point \(A\). Assume \(A=(2,5)\) (from the graph). \(A'=(6,8)\) (from the graph).

Step2: Calculate horizontal shift

Horizontal shift: \(x\) - coordinate change. \(6 - 2=4\) (right - shift as value increased).

Step3: Calculate vertical shift

Vertical shift: \(y\) - coordinate change. \(8 - 5 = 3\) (up - shift as value increased).
Since the same horizontal (\(+4\)) and vertical (\(+3\)) shift will apply to all points of \(\triangle ABC\) (as it is a rigid transformation), the transformation is shifted 4 units right and 3 units up.

Answer:

A. Shifted 4 units right and 3 units up