Question

is stuv similar to bcde? justify your answer.
yes, because a dilation by a scale factor of 3 centered at the origin followed by a reflection over the x - axis maps stuv onto bcde.
yes, because a dilation by a scale factor of 3 centered at the origin followed by a rotation ( 90^{circ} ) clockwise around the origin maps stuv onto bcde.
no, because ( \frac{bc}{st} ) is not equal to ( \frac{de}{uv} )

Explanation:

Step1: Find the lengths of corresponding sides

Assume \(BC\) and \(ST\), \(DE\) and \(UV\) are corresponding sides.
Let's count the units. Suppose \(BC = 3\) units (from \(x=- 2\) to \(x = 1\) in \(BCDE\) for a horizontal side), \(ST=\frac{3}{3}=1\) unit (if we assume a scale - factor consideration). But actually, using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For \(BC\): if \(B(-2,1)\) and \(C(1,1)\), \(BC=\vert-2 - 1\vert=3\). For \(ST\): if \(S(-2,-3)\) and \(T(-2,-1)\), \(ST=\vert-3+1\vert = 2\). For \(DE\): if \(D(3,2)\) and \(E(-3,2)\), \(DE=\vert3 + 3\vert=6\). For \(UV\): if \(U(-1,1)\) and \(V(0,1)\), \(UV = 1\). \(\frac{BC}{ST}=\frac{3}{2}\), \(\frac{DE}{UV}=\frac{6}{1}=6\). Since \(\frac{BC}{ST}
eq\frac{DE}{UV}\).

Answer:

No, because \(\frac{BC}{ST}\) is not equal to \(\frac{DE}{UV}\)