Question

Two similar triangles are shown on the coordinate grid:

A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 2, negative 1, vertex B on ordered pair 0, 0, and vertex C on ordered pair 1, negative 3. A triangle A prime B prime C prime is also shown with vertex A prime on ordered pair negative 4, 2 , vertex B prime on ordered pair 0, 0 and vertex C prime on ordered pair 2, 6.
Which set of transformations has been performed on triangle ABC to form triangle A′B′C′? (5 points)

Dilation by a scale factor of 4 followed by reflection about the x-axis
Dilation by a scale factor of 2 followed by reflection about the x-axis
Dilation by a scale factor of 4 followed by reflection about the y-axis
Dilation by a scale factor of 2 followed by reflection about the y-axis

Answer 1

The set of transformation is: (b) dilation by a scale factor of 2 followed by reflection about the x-axis

The coordinates of the triangles are given as:

Triangle ABC

$A =(-2, -1)$

$B =(0, 0)$

$C =(1, -3)$

Triangle A'B'C'

$A' = (-4, 2)$

$B '=(0, 0)$

$C '=(2, 6)$

Start by dilating triangle ABC by a scale factor of 2.

The rule of this transformation is $(x,y) \to (2x,2y)$

So, we have:

$A' =(-4,-2)$

$B' =(0,0)$

$C' = (2,-6)$

Next, we reflect the triangle across the x-axis.

The rule of this transformation is $(x,y) \to (x,-y)$

So, we have:

$A' = (-4, 2)$

$B '=(0, 0)$

$C '=(2, 6)$

Hence, the set of transformation is: (b) dilation by a scale factor of 2 followed by reflection about the x-axis

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