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)
Accepted Solution
A:
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.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 [tex]\frac{AC}{ZY}[/tex] = [tex]\frac{BC}{XY}[/tex] = 2We can find the length of AC,ZY,BC and XY by using distance formula.Distance formula =[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex] AC=[tex]\sqrt{(4-2)^2+(10-2)^2}[/tex] = Approx 8 BC=[tex]\sqrt{(-6-2)^2+(4-2)^2}[/tex] =Approx 8For triangle XYZ ZY=[tex]\sqrt{(2-1)^2+(5-1)^2}[/tex]=Approx 4 XY=[tex]\sqrt{(-3-1)^2+(2-1)^2}[/tex]=Approx 4[tex]\frac{AC}{ZY}[/tex] = [tex]\frac{BC}{XY}[/tex] = 2Similar 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.