Polygons ABCD and EFGH are similar. What is the perimeter of EFGH?

1 answer:

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If polygons ABCD and EFGH are similar, then their perimeters most likely are also similar. Polygon EFGH also have the same perimeter with polygon ABCD. Having similar polygons is referred as congruent polygons. Two figures are said to be congruent when they have the same shape and size or if one object is a mirror image of the other object.

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Which graph shows the result of dilating this figure by a factor of 4 about the origin? On a coordinate plane, rectangle A B C D

Andrei [34K]

Answer:

Second option: On a coordinate plane, rectangle A'B'C'D' prime has points $(-4,4),(12,4),(12,-4),(-4,-4)$

(See the graph attached)

Step-by-step explanation:

For this exercise it is importnat to know that a Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) has the same shape as the Pre-Image (which is the original figure before the transformation), but they have different sizes.

In this case, you know that the vertices of the rectangle ABCD ( The Pre-Image) are the following:

$A(-1,1)\\\\B(3,1)\\\\C(3,-1)\\\\D(-1,-1)$

Therefore, to find the vertices of the rectangle A'B'C'D' (The Image) that results of dilating the rectangle ABCD by a factor of 4 about the origin, you need to multiply the coordinates of each original vertex by 4. Then, you get:

$A'=((-1)(4),(1)(4))=(-4,4)\\\\B'=((3)(4),(1)(4))=(12,4)\\\\C'=((3)(4),(-1)(4))=(12,-4)\\\\D'=((-1)(4),(-1)(4))=(-4,-4)$