For this question, you must solve for x.
1 answer:
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Answer:
F is the midpoint of AA' because Line E G bisects AA'
Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
we know that
When reflecting a figure, the image is congruent to the pre-image.
A reflection maps every point of the pre-image to an image across a fixed line. The fixed line is called the line of reflection.
The distance of each point of the pre-image from the line of reflection will be the same as the distance of each point of image from the line.
In this problem the line of reflection is E G
The distance A F is equal to the distance A'F
Point F is the midpoint segment A A'
so
Line segment E G bisects segment A A'
therefore
F is the midpoint of A A' because Line E G bisects A A'
Imagine right triangle PHF, where P - park, H - home and F - football field, then PH, PF are legs and HF is hypotenuse . Denote point L to be library. You know that point L lies on the segment FH and FL=8, LH=2. Also you know that PL is an altitude to the hypotenuse.
Use the property of altitude drawn from the vertex of right angle to the hypotenuse (the length of the altitude is geometrical mean between legs' projections onto hypotenuse):
mi.
This means that the distance between park and libriry is 4 miles.
Consider right triangle PLF ( angle L is right angle and PF - hypotenuse). By the Pythagorean theorem,
mi. The distance between park and football field is
miles.
Answer: the distance between park and libriry is 4 miles and the distance between park and football field is miles.