Figures in the Coordinate Plane

The x-axis and y-axis are lines of symmetry for a square. If one of its vertices has coordinates ( a, b), then the vertice opposite it is

(- a, -b)

A base of a parallelogram is on the x-axis and the origin is located at the left endpoint of that base. Three consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0. How many units to the right of a vertical line through (k, 0) must the fourth vertex be?

h

A base of a parallelogram is on the x-axis and the origin is located at the left endpoint of that base. Three consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0. How many units to the right of the y-axis is the point (h, j)?

h

The x-axis contains the base of an equilateral triangle RST. The origin is at S. Vertex T has coordinates (2h, 0) and the y-coordinate of R is g, with g > 0. The x-coordinate of R is

h

The base of an isosceles triangle is parallel to the x-axis. The y-axis passes through an endpoint of the base. If the endpoints of the base are (0, t) and (j, t), what is the x-coordinate of the last vertex of the triangle?

1/2j

If the coordinate axes contain two sides of a square ABCD such that A(0, a) and B(0, 0) are two vertices of the square, then point C is (a, a).

False

The position of a figure in the coordinate plane can make the proof more difficult.

True

A base of a parallelogram is on the x-axis and the origin is located at the left endpoint of that base. Three consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0. What is the y- coordinate of the fourth vertex?

j

A base of a parallelogram is on the x-axis and the origin is located at the left endpoint of that base. Three consecutive vertices are (h, j), (0, 0), and (k, 0), where h > 0. What is the x-coordinate of the fourth vertex?

k+h