Question

quadrilateral qrst is the image of quadrilateral qrst after a translation.
a. if the perimeter of qrst is about 12.4 units, what is the perimeter of qrst?
b. if m∠s = 115°, what is m∠s?
click the icon to view the quadrilaterals qrst and qrst.
a. the perimeter is about \\(\square\\) unit(s).
(type an integer or a decimal)

Explanation:

Part (a)

Step 1: Recall Translation Properties

Translation is a rigid transformation, which means it preserves the shape and size of the figure. So, the lengths of all sides of quadrilateral \(QRST\) and its image \(Q'R'S'T'\) are equal.

Step 2: Determine Perimeter

Since the perimeter is the sum of the lengths of all sides, and the side lengths are preserved under translation, the perimeter of \(Q'R'S'T'\) is equal to the perimeter of \(QRST\). Given the perimeter of \(QRST\) is about \(12.4\) units, the perimeter of \(Q'R'S'T'\) is also about \(12.4\) units.

Part (b)

Step 1: Recall Translation Properties

Translation is a rigid transformation, which means it preserves the angle measures of the figure. So, the measure of \(\angle S\) in quadrilateral \(QRST\) and the measure of \(\angle S'\) in its image \(Q'R'S'T'\) are equal.

Step 2: Determine Angle Measure

Given \(m\angle S = 115^{\circ}\), by the property of translation (preservation of angle measures), \(m\angle S'=115^{\circ}\).

Answer:

s:
a. The perimeter is about \(\boldsymbol{12.4}\) unit(s).
b. \(m\angle S'=\boldsymbol{115^{\circ}}\)