Question

Two similar triangles are shown on the coordinate grid:

Which set of transformations has been performed on triangle MNO to form triangle M'N'O'?

Dilation by a scale factor of 2 followed by reflection about the x-axis
Dilation by a scale factor of fraction 1 over 2 followed by reflection about the x-axis
Dilation by a scale factor of 2 followed by reflection about the y-axis
Dilation by a scale factor of fraction 1 over 2 followed by reflection about the y-axis

Answer 1

D is the correct answer.

Answer 2

Answer: Dilation by a scale factor of fraction 1 over 2 followed by reflection about the y-axis

Explanation:

From the given picture, it can be seen that there must be reflection of triangle across y axis, as reflection flips the figure across the line of reflection.

When we flip back the figure, we will get the coordinates of M = (-1,2)

We know that the vertices of a figure (x,y) after dilation with scale factor k will become (kx,ky).

i.e.
`k=\frac{\text{ x-coordinate of image}}{\text{ x-coordinate of pre-image}}`

From the given picture, in pre-image the x-coordinate of the M =-2

Before reflection across y axis ,

In image, the x-coordinate of M'=-1

Now,
`k=(-1)/(-2)=(1)/(2)`

Hence, the set of transformations has been performed on triangle MNO to form triangle M'N'O': Dilation by a scale factor of fraction 1 over 2 followed by reflection about the y-axis.