Question

(Please this is URGENT!) On a computer screen, Jennifer just created a triangular design of a banner with vertices at A(-4,3), B(-1,5) and C(-1,2). She can use the computer software to perform transformations on this design.

Which sequence of two transformations could she perform so that the transformed vertices become A'(4,-5), B'(7,-7), and C'(7,-4)?


a. translating 6 units down, followed by translating 8 units to the right

b. reflecting about the line y = -2, followed by translating 8 units to the right

c. reflecting about the line y = -1, followed by reflecting about the y-axis

d. reflecting about the line y = -1, followed by translating 8 units to the right

Answer 1

Answer:

The correct option is;

d. Reflecting about the line y = -1, followed by translating 8 units to the right

Step-by-step explanation:

The coordinates of the vertices of the banner Jane created = A(-4, 3), B(-1, 5) and C(-1, 2)

By reflecting across the line y = -1, we get

A(-4, 3) by reflection across the line y = -1 gives A(-4, -5)

B(-1, 5) by reflection across the line y = -1 gives B(-1, -7)

C(-1, 2) by reflection across the line y = -1 gives C(-1, -4)

By translating 8 units to the right get

A(-4, 3) by translation 8 units right gives A prime (4, -5)

B(-1, 5) by translation 8 units right gives B prime (7, -7)

C(-1, 2) by translation 8 units right gives C prime (7, -4)

Therefore, the two transformation that she could perform so that the transformed vertices become A prime (4, -5), B prime (7, -7), and C prime (7, -4) are;

1) Reflection across the line y = -1

2) An horizontal translation 8 units to the right get.

Answer 2

Transformation involves changing the size and position of a shape.

The sequence of two transformations are: (d). reflecting about the line y = -1, followed by translating 8 units to the right

The coordinates of ABC are given as:

$\mathbf{A =(-4,3)}$

$\mathbf{B =(-1,5)}$

$\mathbf{C =(-1,2)}$

First, the coordinates of ABC are reflected across the line $\mathbf{y =-1}$

The transformation rule is:

$\mathbf{(x,y) \to (x,-y -2 \times 1)}$

So, we have:

$\mathbf{A' = (-4,-3 -2 \times 1)}$

$\mathbf{A' = (-4,-5)}$

$\mathbf{B' =(-1,-5 - 2 \times 1)}$

$\mathbf{B' =(-1,-7)}$

$\mathbf{C' =(-1,-2 -2 \times 1)}$

$\mathbf{C' =(-1,-4)}$

Next, the shape is translated 8 units right.

The rule of this transformation is:

$\mathbf{(x,y) \to (x + 8, y)}$

So, we have:

$\mathbf{A" = (-4 + 8, -5)}$

$\mathbf{A" = (4, -5)}$

$\mathbf{B" =(-1+8,-7)}$

$\mathbf{B" =(7,-7)}$

$\mathbf{C" =(-1+8,-4)}$

$\mathbf{C" =(7,-4)}$

Hence, the sequence of two transformations are:

(d). reflecting about the line y = -1, followed by translating 8 units to the right

Read more about transformations at:

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