Question

in the diagram, $\triangle abccong\triangle wrs$. what is the perimeter of $\triangle wrs$?

Explanation:

Step1: Calculate the length of \(AB\)

Since \(A(-5,4)\) and \(B(-5,1)\), using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) (or for vertical line \(x\) - coordinate is same, \(AB=\vert4 - 1\vert = 3\) units.

Step2: Calculate the length of \(BC\)

Since \(B(-5,1)\) and \(C(0,1)\), using the distance formula (or for horizontal line \(y\) - coordinate is same, \(BC=\vert- 5-0\vert = 5\) units.

Step3: Calculate the length of \(AC\)

Using the distance formula \(AC=\sqrt{(0 + 5)^2+(1 - 4)^2}=\sqrt{25 + 9}=\sqrt{34}\approx5\) units (by counting grid - squares and Pythagorean theorem: \(a = 5\), \(b=3\), \(c=\sqrt{5^{2}+3^{2}}=\sqrt{25 + 9}=\sqrt{34}\approx5\)).
The perimeter of \(\triangle ABC\) is \(P_{ABC}=AB + BC+AC=3 + 5+5 = 13\) units.

Step4: Use the property of congruent triangles

Since \(\triangle ABC\cong\triangle WRS\), the perimeters of congruent triangles are equal. So \(P_{WRS}=P_{ABC}\)

Answer:

13 units