Question

what is the measure of angle rst after the dilation of a scale factor of 4? a 30° b 45° c 60° d 90°

Explanation:

Step1: Recall the property of dilation

Dilation is a transformation that changes the size of a figure but not its shape. Angles are preserved in dilation.

Step2: Determine the measure of the original angle

From the grid, we can observe that the original angle (before dilation) has a measure of \(45^{\circ}\) (by using the concept of right - angled triangles formed by the grid lines. If we consider the horizontal and vertical components of the vector forming the angle, they are equal in length. In a right - triangle, if the opposite and adjacent sides are equal (\(a = b\)), then \(\tan\theta=\frac{a}{b}=1\) and \(\theta = 45^{\circ}\) using the formula \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)).

Answer:

B. \(45^{\circ}\)