smokemicpot
contestada

∆ABC is reflected about the line y = -x to give ∆A'B'C' with vertices
A'(-1, 1), B'(-2, -1), C(-1, 0). What are the vertices of ∆ABC?
A.
A(1, -1), B(-1, -2), C(0, -1)
B.
A(-1, 1), B(1, 2), C(0, 1)
C.
A(-1, -1), B(-2, -1), C(-1, 0)
D.
A(1, 1), B(2, -1), C(1, 0)
E.
A(1, 2), B(-1, 1), C(0, 1)

Respuesta :

sqdancefan

That reflection changes (x, y) to (-y, -x). Finding the value of either point A or point B will tell you the correct answer. A will be (-1, 1), as it is on the line of reflection. It is reflected to itself. Thus, the appropriate choice is ...

... B. A(-1, 1), B(1, 2), C(0, 1)

Answer:

Option: B is the correct answer.

            B.          A(-1, 1), B(1, 2), C(0, 1)

Step-by-step explanation:

We know that when a point or a figure is reflected across the line y=x then each of the vertices of the figure i.e. (x,y) is transformed to (y,x)

i.e.   (x,y) → (y,x)

and when the figure is reflected across the line y= -x then each of the vertices of the figure i.e. (x,y) is transformed to (-y,-x)

i.e.   (x,y) → (-y,-x)

Here, the vertices of the transformed figure are:

A'(-1, 1), B'(-2, -1), C(-1, 0).

Let the vertices of A be (x,y)

This means that the vertices of A' are: (-y,-x)

i.e.

(-y,-x)=(-1,1)

i.e.

-y= -1 and -x =1

i.e.

y=1 and x= -1

Hence, the vertices of A are: A(-1,1)

Similarly

Let the vertices of B be (x,y)

This means that the vertices of B' are: (-y,-x)

i.e.

(-y,-x)=(-2,-1)

i.e.

-y= -2 and -x = -1

i.e.

y=2 and x= 1

Hence, the vertices of B are: B(1,2)

Similarly

Let the vertices of C be (x,y)

This means that the vertices of C' are: (-y,-x)

i.e.

(-y,-x)=(-1,0)

i.e.

-y= -1 and -x = 0

i.e.

y=1 and x= 0

Hence, the vertices of  C are: C(0,1)

Otras preguntas