Question

Is triangle A'B'C' a dilation of triangle ABC? Explain.

A) Yes, it is an enlargement with a scale factor of 3.
B) Yes, it is an enlargement with a scale factor of .
C) No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
D) No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.

Answer 1

C) No, it is not a dilation because the points of the image are not moved away from the centre of dilation proportionally.

Explanation:

Dilation is a transformation in which we obtained an image that is the same shape as the original, but different in size.

In dilation we have the scale factor and the centre of the dilation.

Also, if O be the centre about which the point P is dilated to P',

Then
`(OP')/(OP)=k`

Where,

k = scale factor ( constant ),

Thus, we can say that,

If ABC dilated to A'B'C' about the point P,

Then,

`(PA')/(PA)=(PB')/(PB)=(PC')/(PC)`

But,

By the given diagram,

PA = 2 unit, PA' = 6 unit, PB = 3 unit, PB' = 8,

`\because (6)/(2)\\eq (8)/(3)`

Hence, it is not a dilation because the points of the image are not moved away from the centre of dilation proportionally.

Answer 2

Answer: C) No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.

Explanation:

We know that in dilation , to find the points of the image are moved away from the center of dilation proportionally.

Let us assume that Δ A'B'C' a dilation of ΔABC.

Therefore, we have

`(PA')/(PA)=(PC')/(PC)\\\\\Rightarrow(2+4)/(2)=(3+5)/(3)\\\\\Rightarrow3=(8)/(3)..............\rightarrow\text{which is not possible}`

Hence, Δ A'B'C' is not a dilation of ΔABC.