Johnny uses a mirror placed on level ground to measure the height of a building. Johnny's eyes are 6 feet above the ground and h
e stands 4 feet away from the mirror. From that distance, Johnny is able to see the top of the building in the mirror as shown in the diagram below.
If the mirror is 45 feet away from the building’s base, how tall is the building
please show step by step
If the mirror is 45 feet away from the building’s base, how tall is the building
please show step by step
2 answers:
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Answers:
- (12, 3)
- (-4, 3)
- (4, 11)
- (4, -5)
A diagram is shown below.
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Explanation:
First we locate point B at (4,3). The '4' in the x position means we've gone 4 units to the right of the origin, and the 3 in the y coordinate means we've gone 3 units up.
Now we need to find four points that are 8 units away from this central location. We'll ignore point A.
What we can do is add 8 to the x coordinate of point B to get x+8 = 4+8 = 12. Keeping the y coordinate the same, the point (12, 3) is exactly 8 units away from (4,3). Think of drawing a number line through those two points. Then we can note there are 8 spaces between (4,3) and (12,3). Or we can say "there are 8 spaces between 4 and 12" since that '3' doesn't really play much of a role in this case.
So (12,3) is one answer.
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Move back to point B(4,3)
Instead of adding 8 to the x coordinate, let's subtract 8 from it
x-8 = 4-8 = -4
Again the y coordinate is kept the same.
The point (-4, 3) is 8 units away from (4,3). The number line distance from -4 to 4 is 8 units.
So (-4,3) is another answer.
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Move back to point B
From this starting point, we can move 8 units up. Doing this means we add 8 to the y coordinate, while the x coordinate is kept intact.
(4,3) turns into (4,11) after doing so.
(4,11) is another answer.
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Move back to point B
From this point, we can move down 8 units to arrive at (4,-5). note how y-8 = 3-8 = -5. The x coordinate is kept the same.
(4,-5) is another answer.
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The four points we found were:
- (12, 3)
- (-4, 3)
- (4, 11)
- (4, -5)
which are four possible answers
Those points are found by going 8 units right, 8 units left, 8 units up and 8 units down in that order. Each time we started at point B as our center of operation. The use of the word "center" is done because we can form a circle of radius 8, and the center of the circle is at B(4,3). Any point on the circle's edge is exactly 8 units away from the center point B.
Refer to the diagram below. The four answers are the red points P,Q,R,S. The point T is another point that could be an answer, but it's not as easy to find compared to the four other points.
