a'(-1, 1), b(-2, -1), c(-1,0). what are the vertices of aabc?

o a. a(1, -1), b(-1, -2), c(0, -1).

o b. a(-1, 1), b(1, 2), (0, 1)

o c. a(-1,-1), b(-2, -1), c(-1,0)

d. a(1, 1), b(2, -1), (1, 0)

e. a(1, 2), b(-1, 1), co, 1)

Points reflected across x = -1 will be the same distance from it but on the opposite side. The y-values will stay the same for the reflected point. So you can cross out the 2nd and 4th options because they have different y-values. That leaves us with the 1st and 3rd options:

A(0, -1) and A'(4, -1)

See if the x-values are the same distance from -1.

|0 - (-1)| = 1

|4 - (-1)| = 5

The distances are different so let's try the other one:

A(-5, 0) and A'(3, 0)

See if the x-values are the same distance from -1.

|-5 - (-1)| = 4

|3 - (-1)| = 4

The distances are the same, so these points correctly demonstrate a pre-image that has been reflected over x = -1.

A(0, -1) and A'(4, -1)

See if the x-values are the same distance from -1.

|0 - (-1)| = 1

|4 - (-1)| = 5

The distances are different so let's try the other one:

A(-5, 0) and A'(3, 0)

See if the x-values are the same distance from -1.

|-5 - (-1)| = 4

|3 - (-1)| = 4

The distances are the same, so these points correctly demonstrate a pre-image that has been reflected over x = -1.

Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4

Part B:

P''(-1, 0)

Q''(0, -1)

R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are not congruent

Step-by-step explanation:

The coordinates of triangle PQR are;

P(4, 0)

Q(0, 4)

R(-8, -4)

The coordinates of triangle P'Q'R' are;

P'(1, 0)

Q'(0, -1)

R'(-2, -1)

Part A:

The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' can be found from the ratio of the respective coordinates as follows;

The ratio of the x, and y coordinates of the points are;

P'/P = x'/x = 1/4, y'/y =0/0

R'/R = x'/x = -2/-8 = 1/4, y'/y =-1/-4 = 1/4

Therefore, the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' = 1/4

Part B: For reflection across the y-axis, we have;

Pre-image (x, y) becomes the image, (-x, y)

Therefore, we have;

Reflection of P'(1, 0) about the y-xis becomes P''(-1, 0)

Reflection of Q'(0, -1) about the y-xis becomes Q''(0, -1)

Reflection of R'(-2, -1) about the y-xis becomes R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are similar but they are not congruent as the dimensions of PQR are larger than the dimensions of the sides of triangle P''Q''R''.

B

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x ), thus

J(0, - 3 ) → J'(- 3, 0 )

K(- 1, 0 ) → K'(0, - 1 )

L(- 2, - 1 ) → L'(- 1, - 2 )

a) It is dilated by a factor of 1/4

b) P"(-1, 0), Q"(0, -1), R"(2, -1)

c) They are not congruent

Step-by-step explanation:

Triangle PQR has verticals P(4,0) Q(0,-4) R(-8,-4). Triangle P'Q'R' has verticals P'(1,0) Q'(0,-1) and R'(-2,-1)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, dilation and translation.

Dilation is the reduction or enlargement of an object. If a point X(x, y) is dilated by a factor of k ,the new location is X'(kx, ky).

If a point X(x, y) is reflected about the y-axis, the new location is X'(-x, y)

a) Triangle PQR has verticals P(4,0) Q(0,-4) R(-8,-4) is dilated by a factor of 1/4, the new location would be P'(1,0) Q'(0,-1) and R'(-2,-1).

b) If triangle P'Q'R' is reflected about the y axis, the new location is P"(-1, 0), Q"(0, -1), R"(2, -1)

C) Two triangles are congruent if they have the same sides and angle. Triangle PQR and triangle P"Q"R" are not congruent because triangle PQR is smaller than triangle P"Q"R"

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