Which of the following is the rule for rotating the point with coordinates (x,y), 180° counterclockwise about the origin?
2 answers:
Answer:
The correct option is D.
Step-by-step explanation:
If a point rotating 180° counterclockwise about the origin, then the sign of each coordinate is changed.
Consider the coordinates of a point are (x,y).
If a (x,y) rotating 180° counterclockwise about the origin, then the rule of rotation is defined as
In which (x,y) is the coordinate pair of preimage and (-x,-y) is the coordinate pair of image.
Therefore the correct option is D.
If a point reflects across the line y=x , then
If a point rotated 90° clockwise, then
If a point reflects across the line y=-x, then
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The Pythagorean's Theorem for our situation would look like this:
So let's call the short leg s, the long leg l and the hypotenuse h. It appears that all our measurements are based on the measurement of the short leg. The long leg is 4 more than twice the short leg, so that expression is l=2s+4; the hypotenuse measure is 6 more than twice the short leg, so that expression is h=2s+6. And the short leg is just s. Now we can rewrite our formula accordingly:
And of course we have to expand. Doing that will leave us with
Combining like terms we have
Our job now is to get everything on one side of the equals sign and solve for s
That is now a second degree polynomial, a quadratic to be exact, and it can be factored several different ways. The easiest is to figure what 2 numbers add to be -8 and multiply to be -20. Those numbers would be 10 and -2. Since we are figuring out the length of the sides, AND we know that the two things in math that will never EVER be negative are time and distance/length, -2 is not an option. That means that the short side, s, measures 10. The longer side, 2s+4, measures 2(10)+4 which is 24, and the hypotenuse, 2s+6, measures 2(10)+6 which is 26. So there you go!