Question

What are the coordinates of the vertices of each figure?

7) rectangle with base 'b' and height 'h'
8) square with sides of length 'a'
9) square centered at the origin, w/ side length 'b'
10) parallelogram where 'S' is 'a' units from the origin and 'Z' is 'b' units from the origin
11) rhombus centered at the origin, with SW = 2 and TZ = 2t
12) isosceles trapezoid with base centered at origin, w/ base 2a and OR = 'c'

Answer 1

7.) The coordinates of the given rectangle are O(0, 0), S(0, h), T(b, h), W(b, 0)

8.) The coordinates of the given square are O(0, 0), S(0, a), T(a, a), W(a, 0)

9.) The coordinates of the given square are S(-b/2, -b/2), T(-b/2, b/2), W(b/2, b/2), Z(b/2, -b/2)

Answer 2

Part 7)
`O(0,0),S(0,h), T(b,h), W(b,0)`

Part 8)
`O(0,0),S(0,a), T(a,a), W(a,0)`

Part 9)
`S(-b/2,-b/2),T(-b/2,b/2),W(b/2,b/2),Z(b/2,-b/2)`

Part 10)
`Z(b,0), W(b+c,0),T(c,a),S(0,a)`

Part 11)
`W(r,0),T(0,t),S(-r,0),Z(0,-t)`

Part 12)
`S(-a,0),Z(a,0),W(b,c),T(-b,c)`

Explanation:

Part 7) we know that

The point O is at origin

so its coordinates are
`O(0,0)`

Since the height of the rectangle is h, S and T are h units away from the x-axis

Since the base is b, T and W are b units away from the y-axis

thus the coordinates of the other vertices are

`S(0,h), T(b,h), W(b,0)`

Part 8) we know that

The point O is at origin

so its coordinates are
`O(0,0)`

Since the height of the square is a, S and T are a units away from the x-axis

Since the base is also a, T and W are a units away from the y-axis

thus the coordinates of the other vertices are

`S(0,a), T(a,a), W(a,0)`

Part 9) we know that

Since the square STWZ is centered at the origin and side length is b, S and T are b/2 units away from each axis

The same is true for the other vertices

so

`S(-b/2,-b/2),T(-b/2,b/2),W(b/2,b/2),Z(b/2,-b/2)`

Part 10) we know that

Since the parallelogram has height a, S and T are a units away from the x-axis

The x-coordinate of T and W do not depend on a or b, so use a different variable c for T and W

Thus

`Z(b,0), W(b+c,0),T(c,a),S(0,a)`

In this part another variable for c is acceptable

Part 11) we know that

Since the rhombus STWZ is centered at the origin, the diagonal be on the axes and the diagonals bisect each other, T and Z are t units away from the x-axis, and S and R are r units away from the y-axis

so

`W(r,0),T(0,t),S(-r,0),Z(0,-t)`

Part 12) we know that

Since the the base of the isosceles trapezoid is centered at the origin, S and Z are a units away from the y-axis

The height is c , so T and W are c units away from the x-axis

The distance of T and W from the y-axis, do not depend on a or c, so another variable b is needed

Therefore

`S(-a,0),Z(a,0),W(b,c),T(-b,c)`

In this part another variable for b is acceptable