Analytic Geometry Review

Midpoint & Distance Formula

100

What is the distance between the points A(14,-3) and B(2,2)?

13

200

What is the distance between C(-1,-4) and D(6,2)?

9.219

300

Two coordinates of a line are A(2,4) and B(6,3). Their midpoint is .....

(4, 7/2)

400

The midpoint of a line is (-3,5). It is between the points C(-2,y) and D(x,-8). What are the values of x and y?

x= - 4 and y=18

500

A skydiver lands 150 yards west and 30 yards north of a target. A second skydiver lands 45 yards east and 150 yards south of the same target. How far from each other did the two skydivers land?

265.4

Find Median, Perpendicular Bisector or Altitude

100

For the triangle with vertices A(0,0), B(6,11), and C(12,5). What is the slope of the median from vertex A?

m = 8/9

200

For the triangle with vertices A(0,0), B(6,11), and C(12,5). What is the slope of the perpendicular bisector of BC?

m = 1

300

For the triangle with vertices A(0,10), B(-14,-4) and C(8,0). Find the equation for the median from vertex B.

y=(1/2)x+3

400

For the triangle with vertices A(1,6), B(-7,-6), and C(7,-6). What is the equation for the perpendicular bisector for AB?

y=-(2/3)x-2

500

For the triangle with vertices A(-4,4), B(2,3), and C(-6,-5). What is the equation for the altitude from point A?

y = -x

Classify Shapes

100

Some squares are rhombuses.

True or False?

False; all squares are rhombuses and some rhombuses are squares (if they have four right angles)

200

Given triangle ABC with A(0, 5), B(0, -5), and C(-3, 3) classify the triangleas equilateral, isosceles, or scalene.

Scalene

300

 Quadrilateral ABCD has coordinates A(4,7), B(9,7), C(6,3), and D(1,3). What kind is it?

Rhombus

400

A triangle has vertices at P (-2,2) , Q (1,3) and R (4,-1). Find the slope and length of the midsegment joining the midpoints of PQ and PR.

m = -4/3

l = 2.5 units

500

A triangle has vertices at A (-1,-1) , B (2,0) and C(1,3).  Classify the triangle.

Isosceles Right Triangle

Shortest Distance

100

What is the distance between point A(-2,4) and the line y=x?

4.242

200

Determine the shortest distance from the point D(2,−5) to the line represented by y = 3

8

300

What is the distance from the point A(4,4) and the line segment that passes through the points D(-3,3) and E(5,-3)?

5

400

Find the distance between point  (-1, -3) and the midpoint of the line segment joining (2, 4) and (4,6).

8.94

Equation of a Circle

100

What is the radius of the circle given by x²+y²=64?

8

200

Does the point (-7,-1) lie inside, on or outside the circle given by x²+y²=49?

Outside

300

What is the equation of the circle upon which the point (-10, 6) lies on?

x²+y²=136

400

What is the equation of the circle whose diameter endpoints are (-5,12) and (5,-12)?

x²+y²= 169