The point A(-6,6) is reflected over the point (0,7) and its image is point B. What are the coordinates of point B?

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Explanation:

Let's label (0,7) as point C.

Plot points A and C on the same coordinate system.

Note that to go from A to C, we must do two things (in either order)

These two items will be replicated in either order to go from point C to point B.

The translation rule we follow is which is a mathematical way of saying "go right 6 and up 1". If we plug in x = -6 from point A we get to x = 0 which is the x coordinate of point C. Repeating this leads to x = 6, which is the x coordinate of point B.

Through similar arguments, we go from y = 6, to y = 7, to y = 8, when we hop from points A, to C, to B in that exact order.

Put everything together and we see that B is located at (6,8)

The diagram below provides a visual summary.

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Extra info:

If we draw a line from point A to B, then point C will be on this line. Furthermore, AC = CB which can be proven using congruent triangles. Reflections preserve distance, meaning the distance from A to the mirror point C, is the same as from B to C as well. In short, we can say C is the midpoint of segment AB.

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.