Problem Set-analytic Geometry

PROBLEM SET (Analytic Geometry) I.

Solve, interpret geometrically and graph the following. When applicable, write answers using both inequality notation and interval notation. 1. x ≥ 5

II.

2.  x < 5

3.  y-5 ≤ 5

Solve and graph the following. Write answers using both inequality notation and interval notation. 1. x2< 1-3x

III.

2. x2≤ 8x

3. [(x-2)/(x+4)]<0

4.[(x-2)2/(x2+2-3)] ≤ 0

Supply and graph the equation of the line which satisfies the given conditions: 1. Horizontal; y-intercept is 2 2. Vertical; x-intercept is 4

IV.

Determine an equation of the line through the given point and with the given slope; or through the given point and with the given inclination; or through the two given points. Graph each equation of the line. 1. (8, -2); m =

2 3

2. (-1, 4); m =

3 4

3. (-4, 6); (5, -3)

4. (-5, 3); (4, 6)

5. (1, 4); φ = 150o

6. (9, -1); φ = 30o

V.

Give the intercepts and the slope of the graph of the given equation and graph that equation. 1. 7x + 8y + 10 = 0

VI.

2. x – 3y + 7 = 0

Determine the equation of the line through the point (2, 3) and parallel to the graph of 3x – 2y + 6 = 0.

VII.

Determine an equation of the line through the point of intersection of the graphs of x – 3y + 2 = 0 and 5x + 6y - 4 = 0 that is parallel to the graph of 4x + y = -7.

VIII.

A triangle has 5x – 6x + 16 = 0, x + 7y + 36 = 0, and 6x + y -30 = 0 for equations of its sides. Give the coordinates of the vertices of the triangle. Determine an equation of the perpendicular bisector of each of the sides of the triangle. Show the complete illustration.