Question

Describe a sequence of two transformations, first a translation and then a reflection, that would map ABC onto MNP. There are many correct answers. Be as specific as possible with both transformations.

Answer 1

Transformation involves changing the position of a shape.

The sequence of transformations is:

• Translate triangle ABC 8 units left, and 6 units down
• Reflect the image across the x-axis

From the graph, the coordinates of triangle ABC are:

$A = (2,8)$

$B = (7,8)$

$C = (7,2)$

Start by translating the above points 8 units left and 6 units down.

The rule of this translation is:

$(x,y) \to (x-8,y-6)$

So, we have:

$A' = (-6,2)$

$B' = (-1,2)$

$C' = (-1,-4)$

Next, reflect ABC across the x-axis.

The rule of this reflection is:

$(x,y) \to (x,-y)$

So, we have:

$A" = (-6,-2)$

$B" = (-1,-2)$

$C" = (-1,4)$

From the graph, the coordinates of triangle MNP are:

$M = (-6,-2)$

$N = (-1,-2)$

$P = (-1,4)$

By comparison, the vertices of A"B"C" is the same as the vertices of MNP

Hence, the sequence of transformations is: translate triangle ABC 8 units left, 6 units down and reflect the image across the x-axis

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