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Anuta_ua [19.1K]
3 years ago
12

Which statement is true about a shape and its dilation? A.The corresponding angles of a shape and its dilation are congruent. B.

The corresponding angles of a shape and its dilation are not congruent. C.The side lengths of a dilation are always smaller than the corresponding side lengths of the original shape. D.The corresponding side lengths of a shape and its dilation are congruent.
Mathematics
1 answer:
BartSMP [9]3 years ago
6 0

Answer:

A.The corresponding angles of a shape and its dilation are congruent.

Step-by-step explanation:

Dilation is a type of rigid transformation in which the dimension of a shape is either increased or decreased to produce its image. It involves a change in the dimensions of the shape by a required factor. In the process, the side lengths of the image are different to the original lengths. But the angles are not affected.

Thus, the respective angles of the given shape and its image are the same.

The appropriate answer to the given question is A.

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Part A: Plot the points A(-8,7) and B(6,-9). Mark the halfway point on AB and label it point M. What are the coordinates of M? P
vredina [299]

Answer:

a. M(x,y) = (-1,-1)

b. D(-4,-9)

Step-by-step explanation:

Given

A(-8,7) and B(6,-9).

Solving (a):

Determine the Midpoint M;

This is calculated as follows;

M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Where

(x_1,y_1) = (-8,7)

(x_2,y_2) = (6,-9)

Substitute these values in the formula

M(x,y) = (\frac{-8+6}{2},\frac{7-9}{2})

M(x,y) = (\frac{-2}{2},\frac{-2}{2})

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

<em>Hence; the midpoint is (-1,-1)</em>

Solving (a):

Here, we have

C = (2,7)

M; Midpoint = (-1,-1)

Required: Determine D

This is calculated as follows;

M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Where

(x_1,y_1) = (2,7)

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

Substitute these values in the formula

(-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})

Solving for x2

-1 = \frac{2 + x_2}{2}

Multiply both sides by 2

-2 = 2 + x_2

Subtract 2 from both sides

x_2 = -2 - 2

x_2 = -4

Solving for y2

-1 = \frac{7 + y_2}{2}

Multiply both sides by 2

-2 = 7 + y_2

Subtract 7 from both sides

y_2 = -2 - 7

y_2 = -9

Hence, the coordinates of D is

D(-4,-9)

7 0
4 years ago
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