Chapter 1 Review
Analytical Geometry
Name: ____________________
1) Determine whether (2, 3), (1, 5) and (-1, 9) are collinear.
2) Find the distance between A = (5, 3) and B = (-1, 7).
3) Find the unknown quantity of A = (x, -2) and B = (5, 7) when AB = 3
4) Find the point P between A and B such that A = (2, -5), B = (-3, 4) and
.
.
5) Find the midpoint of A = (4, 9) and B = (-2, -3).
6) If A = (3, 3), P = (5, 2) and
, find B.
7) Find the slope, m, (if any) and the inclination, , of the line through the points (-2, 4) and (1, -6).
8) Determine whether l1 defined by points (1, 3) and (-1, -1) and l2 defined by points (0, 2) and
(4, -2) are parallel, coincident, perpendicular, or none of these.
9) Graph the line through (2, -3) with zero slope.
10) If the line through (x, 5) and (4, 3) is parallel to a line with slope 2, find x.
11) Find the angle from l1 to l2 with slopes m1 = -2 and m2 = 4 respectively.
12) Find the angle from l1 to l2 where l1 goes through (1, 2) and (3, -2) and l2 goes through (-1, 5) and
(-2, 3).
13) Find the slope of the line bisecting the angle from l1 to l2 with m1 = 2 and m2 = 3 respectively.
14) Find the slope of the line bisecting the angle from l1 to l2 where l1 has zero slope and m2 = ½.
15) Find the slope of the line bisecting the angle from l1 to l2 where m1 = ¾ and l2 has no slope.
16) Find the points of intersection and sketch the graphs of the equations 2x + 4y = 12 and
3x – 2y = 6.
17) Find the points of intersection and sketch the graphs of the equations x – y = 5 and y = x2.
18) Find the points of intersection and sketch the graphs of the equations x – 2y = -1 and x2 = 3 – 2y.
19) Find an equation for the set of all points (x, y) such that it is on the line containing (4, 2) and
(2, -1).
20) Find an equation for the set of all points (x, y) such that it is equidistant from (2, 3) and the yaxis.
21) Find an equation for the set of all points (x, y) such that it is twice as far from (-3, 1) as it is from
(3, 0).
22) Find an equation for the set of all points (x, y) such that its distance from (2, 5) is 4.
23) Use distances to determine whether or not the points (1, 6), (5, 3), and (3, 1) are the vertices of
a right triangle. Check your answer using slopes.
24) Determine x such that (x, 1) is on the line joining (0, 4) and (4, -2).
25) Find the points of trisection of the segment joining (2, -5) and (-3, 7).
26) Find an equation of the perpendicular bisector of the segment joining (5, -3) and (-1, 1).
27) The point (5, -2) is at a distance of
(-1, 1). Find y.
from the midpoint of the segment joining (5, y) and
28) Prove analytically that the diagonals of a square intersect at right angles.
29) Prove analytically that the midpoint of the hypotenuse of a right triangle is equidistant from the
three vertices.
30) Prove analytically that the vertex and the midpoints of the three sides of an isosceles triangle
are the vertices of a rhombus.