Geometry - QUIZ 4: FIGURES AND PROOFS

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the slope of the line through the origin and the center.

1

Given the points A(0, 0), B(e, f), C(0, e) and D(f, 0), determine if line segments AB and CD are parallel, perpendicular or neither.

perpendicular

Choose the kind(s) of symmetry: point, line, plane, or none. (8)

plane line

Choose the kind(s) of symmetry: point, line, plane, or none. (B)

plane line

Choose the kind(s) of symmetry: point, line, plane, or none. (0)

point plane line

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.

r√2

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the coordinates of the points of tangency.

(0, r) and (r, 0)

In rectangle ABCD, if the coordinates of A are (0, 0) and of C are (r, s), find the coordinates of B.

(0, s)

Find the coordinates of the other endpoint if the midpoint is M(8, 2) and the other endpoint is P(5, 6).

(11, -2)

Find the coordinates of the center of the given circle. (x - 5) 2 + (y + 3) 2 = 25

(5, -3)

For parallelogram ABCD, A(0, 0), B(a, b), and D(c, 0) are three of its vertices. Find the coordinates of C in terms of a, b, c.

(a + c, b)

In equilateral triangle RST, R has coordinates (0, 0) and T has coordinates of (2a, 0). Find the coordinates of S in terms of a.

(a, a√3)

Find the length of the radius of the given circle. (x - 5) 2 + (y + 3) 2 = 25

5

For a proof which placement of the axes would be least acceptable for a rhombus?

The one where a part of the rhombus is in all four quadrants.

Choose the kind(s) of symmetry: point, line, plane, or none. (A)

line plane

Choose the kind(s) of symmetry: point, line, plane, or none. (C)

line plane

Choose the kind(s) of symmetry: point, line, plane, or none. (7)

none

Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation box below. E (-2, 2), F (5, 1)

x + 7y = 12

Indicate, in standard form, the equation or inequality that is shown by the graph. (Line passing through 0,4 and 4,0)

x + y = 4

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the equation of the line containing the points of tangency.

x + y = r