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Katlynnmarkle13
14.11.2019 •
Mathematics
75 points to whoever does all of this for me.
1. draw, in black, the triangle with vertices (-3, 2), (1, 1), and (2, 5).
2. draw the triangle's image under the dilation (x, y ) → (2x, 2y).
3. explain clearly why the two triangles must be similar.
4. how could a dilation create a figure which is congruent to the original one? [hint: there are two ways.]
(share imgur link)
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Ответ:
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.
Step-by-step 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 =![\sqrt{(x2-x1)^2+(y2-y1)^2}](/tpl/images/0374/7961/aae60.png)
AC=
= Approx 8
BC=
=Approx 8
For triangle XYZ
ZY=
=Approx 4
XY=
=Approx 4
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.
Ответ:
A+m=76
De mai jos scoatem pe a si m in functie de r
m+r=78 => m=78-r
a+r=82 => a=82-r
Inlocuim in prima
82-r+78-r=76
160-2r=76
-2r=76-160
-2r=-84 / -1 pt a scapa de -
2r=84
r=84:2
r=42 ani
De acum e simplu, inlocuim mai sus
m=78-r
m=78-42=36
a=82-42=40