Question

drag each phrase to the correct location on the table.
the following transformations were applied to \\( \triangle a b c \\) on the coordinate plane below to give \\( \triangle j k l \\) and \\( \triangle q r s \\).
\\( \triangle j k l:(x, y) \
ightarrow(x+3, y+2) \\)
\\( \triangle q r s:(x, y) \
ightarrow(2 x, 2 y) \\)
drag the phrase that completes the relationship between \\( \triangle j k l \\) and \\( \triangle q r s \\).
has vertices with the same values as, has vertices with the same values as,
and the same perimeter as and a lesser perimeter than
has vertices with different values than, has vertices with different values than,
and the same perimeter as and a lesser perimeter than
has vertices with different values than, has vertices with the same values as,
and a greater perimeter than and a greater perimeter than

Explanation:

• For \(\triangle JKL\): The transformation \((x,y)\to(x + 3,y+2)\) is a translation. A translation is a rigid - motion transformation. Rigid - motion transformations preserve the shape and size of a figure. So, the vertices of \(\triangle JKL\) have different \(x\) and \(y\) values (because of the shift in the coordinate plane) but the perimeter remains the same as \(\triangle ABC\).
• For \(\triangle QRS\): The transformation \((x,y)\to(2x,2y)\) is a dilation with a scale factor \(k = 2\). When a figure is dilated with a scale factor \(k>1\), the sides of the new figure are \(k\) times the sides of the original figure. The perimeter of a figure is the sum of its side lengths. If the side lengths are multiplied by \(k = 2\), the perimeter of \(\triangle QRS\) is \(2\) times the perimeter of \(\triangle ABC\). So, the vertices of \(\triangle QRS\) have different values (because of the scaling of the coordinates) and a greater perimeter than \(\triangle ABC\).

Answer:

\(\triangle JKL\)	\(\triangle QRS\)