A 100-point math test contained true/false questions worth 3 points each and short answer questions worth 11 points each. If the
1 answer:
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Answer: Check out the diagram below
The reflected image is shown in red.
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Explanation:
Draw a vertical line through -2 on the x axis. This is the mirror line.
Now focus on the upper right corner of the figure, which is at (-3, -1). Notice how the horizontal distance from this corner point to the mirror line is exactly 1 unit. If we move another 1 unit to the right, then we'll arrive at (-1,-1) which is where the reflected point lands or ends up.
In short, the upper right corner point (-3,-1) reflects over x = -2 to land on (-1,-1)
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As another example, the upper left corner point (-5, -1) will move exactly 4 spaces to the right to get to the mirror line. Then we move another 4 spaces to the right to get to (2,-1).
So the upper left corner (-5,-1) will ultimately move to (2,-1) after the reflection over x = -2.
Apply these steps to the other corner points and you'll end up with what is shown below.
Take note that a point like A(-5,-1) moves to A'(1,-1), and similar to the other points as well. Also, notice that when going from A to B to C, etc we are moving clockwise. We move counterclockwise when going from A' to B' to C' etc. Reflections always swap the orientation.
This problem can be solved using the Pythagorean Theorem.
<em>Note: the height of the telephone pole is unnecessary information.</em>
Convert the measurement in feet to inches.
The length from the base of the pole to the anchor point on the ground is inches. The distance from the base of the pole to the anchor point on the pole is
inches.
These are the two legs of a right triangle. The length of the stabilizing cable is the hypotenuse of the right triangle.
The Pythagorean Theorem is:
In this formula, and
are the legs and
is the hypotenuse.
Plug in the known values.
Swap the sides of the equation.
Evaluate the powers.
Simplify using addition.
Take the square root of both sides.
Separate the solutions.
Length and distance cannot be negative, so remove the negative solution.