Answer:
Whenever an image goes under dilation we multiply the co-ordinates of each vertex with a scale factor (k).
Points (x,y) becomes (2x,2y) so the scale factor is 2.
Explanation:
1.The diagram is shown below.
2.The co-ordinates (-3,2),(1,1) and (2,5) will become (-6,4),(2,2) and (4,10).
3.Dilated figures are similar.
The two triangles must be similar as we can see
=
= 2
We can find the length of AC,ZY,BC and XY by using distance formula.
Distance formula =
![√((x2-x1)^2+(y2-y1)^2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/nfczm4e6nctej3ztnzs7dhuhdhqee8lz7i.png)
AC=
= Approx 8
BC=
=Approx 8
For triangle XYZ
ZY=
=Approx 4
XY=
=Approx 4
=
= 2
Similar triangles must have proportional side lengths.
Statement:Two figures are said to be similar when one figure can be obtained from the other by a single transformation that includes translation, reflection, rotation and dilation,the size may not be same.
So in above question the triangles are undergoing dilation with a positive scale factor,hence both are similar.
4.Dilation and congruence.
When the scale factor is equivalent to one (1).
The dilation create a figure which is congruent to the original one.
Similarity preserves shape, but not necessarily size making the figures similar.It is possible for similar figures to have a scale factor of 1 then it can be said that all congruent figures are also similar.