Question

Use the graph to answer the question

Answer 1

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:

`Dis\tan ce=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

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:

`\begin{gathered} (AB)/(EB)=(BC)/(BD)=(CA)/(DE) \\ \text{ Substitute the value:} \\ (7.2)/(3.6)=(6)/(3)=(4)/(2) \\ (2)/(1)=(2)/(1)=(2)/(1) \\ \text{ rato= 2:1} \end{gathered}`

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

`\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}`

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