Algebra I
EOCT Review II: Geometry
GEOMETRY
I. Midpoint: the point that divides a line segment into two equal parts
m=
x1 + x2 y1 + y2
,
2
2
A. Find the midpoint between each pair of numbers.
1) (6, 8) and (3, 4)
2) (-4, 2) and (4, 17)
3) (9, -2) and (3, -6)
B. Given the midpoint and one endpoint, find the other end point.
4) midpoint: ( 2, − 8) , endpoint: ( 7, − 3)
5) midpoint: ( 4, − 6 ) , endpoint: ( 3, − 9 )
6) midpoint: ( 3, − 4 ) , endpoint: ( −7, 2 )
C. Applications
7)
Jennifer and Jane placed a map of their town on a coordinate grid and found the point at which each of their
houses lies. If Jennifer’s house lies at ( 9, 7 ) and Jane’s house is at (15,9 ) and they wanted to meet in the
middle, what are the coordinates of the place they should meet?
II.
Slope - Parallel and Perpendicular Slopes
Parallel lines have the
Perpendicular Lines meet at
slope.
angles and have
slopes.
Slope:
A.
1)
Find the slopes of each pair of lines and determine if the lines are parallel, perpendicular, or neither.
2)
Line 1 goes through ( -2,4) and ( -5,1)
Line 2 goes through ( 2,2) and ( -3,-3)
B.
III.
Line 1 passes through (-2, 2) and (-4, 6)
Line 2 passes through ( -6, -6) and ( 2, -4)
c
. (a) What is the slope of a line parallel to k?
d
(b) What is the slope of a line perpendicular to k?
1)
Suppose a line k in a coordinate plane has slope
2)
(a) What is the slope of a horizontal line? (b) What is the slope of a vertical line?
Point Slope Form of a Line:
Find the equation of each line in slope-intercept form.
1) slope: –5 , through ( 6, −2 )
2) ( 7, −3) and ( −2,7 )
Slope-Intercept Form:
3)
( 0, −4 ) and ( 2, −1)
through ( 2, −1) .
and perp. to this line
IV.
Pythagorean Theorem:
Find the missing side of each triangle.
1)
2)
6
4
9
9
V. Draw each of the following: (a) triangle, (b) parallelogram, (c) rectangle, (d) square, (e) rhombus, (f) trapezoid.
For each of the following, point the points, determine what type of geometric figure it is, and find the perimeter.
2) ( 2,5 ) ( −4,1)( 3, −5)
3) ( 3, 0 )(1,3)( −2,1)( 0, −2 )
1) (1,1) (1,4) (5,4)
4)
If Quadrilateral ABCD is a rectangle, where A (1, 2 ) , B ( 6, 0 ) , C (10,10 ) , and D ( ?,? ) . (a) Plot the points and
find D. (b) Find the slopes of all the sides.
VI.
I.
Formulas
A.
Formula for the circumference of a circle
Formula for the area of a circle
1) Find the circumference of wheel with a radius of 25 cm, and find the area of the same wheel.
B.
Formula for the volume of a cylinder: ________________
2)
Find the volume in terms of π of a cylinder with r = 10, h = 3 .
C.
Formula for the volume of a pyramid: ________________
3)
Find the volume of a square pyramid with side length 5 and height 7.
D.
Formula for the volume of a sphere: _________________
4)
Find the volume of a sphere terms of π with radius 6
E.
Formula for the volume of a cone: ___________________
5)
Find the volume of a cone terms of π with radius 7 and height 3.
Problem:
The volume of a sphere is 2,400 cubic centimeters. What is the approximate diameter of this sphere?
HOMEWORK
1) Find the midpoint between ( 5, −2 ) and ( 6,9 ) .
3)
2) Given the midpoint and one endpoint, find the other end
Point: midpoint: ( −2,5 ) , endpoint: ( 8, − 3)
4)
Line 1 passes through ( -4, -2) and ( -6, 1)
Line 2 passes through ( 0, 5) and ( -3,3)
5)
Find the missing sides of the triangles.
(a)
Line 1 passes through (0,3) and ( 4,4)
Line 2 passes through ( -4,2) and ( -8,1)
(b)
3
5
8
12
6) For each of the following, point the points, determine
what type of geometric figure it is, and find the
perimeter.
( -6, 7) (-6, -5) ( 5, 4) (5, -2)
7) If Quadrilateral ABCD is a rectangle, where
A ( −1,5) , B ( −1, −7 ) , C ( 4,5 ) , and D ( ?,? ) , (a) Plot the
points and find D. (b) Find the slopes of all the sides.
8) Find the circumference and area of each circle. Use 3.14 for π .
1)
2)
3)
Find the volume.
4)
5)
6)