Answer :
Triangle ABC and EBD are similar
The coordinates of triangle ABC are:
A(-6,4)
B(0,0)
C(-6,0)
Similarly the coordinates of EBD is:
E(-2,-3)
B(0,0)
D(0,-3)
The ratio of corresponding sides of similar triangle are equal
So, apply distance formula for the measurement of sides of triangle:
Distance formula is express as:
[tex]Dis\tan ce=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]So, apply distance formula we get
AB : (-6,4) & (0,0), AB=7.2
BC(0,0) & (-6,0), BC=6
CA(-6,4)(-6,0), CA=4
Similarly In triangle EBD
EB(-2,-3),(0,0), EB=3.6
BD(0,0)(0,-3), BD=3
DE(0,-3)(-2,-3)DE=2
The ratio will be:
[tex]\begin{gathered} \frac{AB}{EB}=\frac{BC}{BD}=\frac{CA}{DE} \\ \text{ Substitute the value:} \\ \frac{7.2}{3.6}=\frac{6}{3}=\frac{4}{2} \\ \frac{2}{1}=\frac{2}{1}=\frac{2}{1} \\ \text{ rato= 2:1} \end{gathered}[/tex]Thus, Scale Factor: 2
A dilation includes the scale factor (or ratio) and the center of the dilation. The center of dilation is a fixed point in the plane.
Here the triangles have scale factor of 2 and the dialation point is B(0,0) or origin
The cooridnates of trinagle ABC are in the second quadrant with (-x,y)
and the coordinates of triangle EBd are in third coordinate (-x,-y)
i.e
[tex]\begin{gathered} (-x,y)\rightarrow(-x,-y) \\ In\text{ 90 degr}ee\text{ clockwise: (x,y)}\rightarrow(y,-x) \\ In\text{ 90 degre}e\text{ }counter-clockwise(x,y)\rightarrow(-y,x) \\ \text{Thus, over similar triangle follow the rule of 90 degr}e\text{ counter-clockwise} \end{gathered}[/tex]The triangle is rotated at origin through 90 degree counter clockwise
Answer:
B) rotation 90 counter clockwise about the origin
E) dialation, centered about origin with a scale factor of 2
