Question

What are the coordinates of Z?

Answer 1

Answer: (0,c) which is the third answer choice

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Step-by-step explanation:

Note how the point (a,0) mirrors over the y axis to land on (-a,0)

A similar action will happen as we go from te point (b,c) to point W (-b, c), due to this figure being isosoceles.

The x coordinate changes from positive to negative. The y coordinate stays the same.

The point Z is the midpoint of the upper segment which spans from (-b,c) to (b,c)

Apply the midpoint formula to find where Z is located.

Add up the x coordinates and divide by 2: x = (-b+b)/2 = 0/2 = 0

Add up the y coordinates and divide by 2: y = (c+c)/2 = 2c/2 = c

So the midpoint is located at (x,y) = (0, c) which is where point Z is located as well.

Side note: it might help to replace the letters a, b and c with actual values, just so the problem is more concrete.

Answer 2

The correct answer option is C. (0, c).

Step-by-step explanation:

We are given an isosceles trapezoid with the coordinates of three of its vertices and we are to find the coordinates of Z.

Z is a point on the middle of one of the sides of the trapezoid.

Since Z lies on the horizontal x axis, therefore its x coordinate is 0 while the y coordinate can be seen from the vertex exactly at its right which is c.

Z (0, c)