Liberal Art Mathematics
bderisse
Unit6Test.pdf
Unit 6: Is There a Point to This?342
Practice
For each of the following:
• plot the two points
• draw the hypotenuse
• complete the triangle
• use the Pythagorean theorem to find the distance between the given points
• show all your work
• leave answers in simplest radical form.
1. (3, 4), (-2, 6)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This? 343
2. (3, -3), (6, 4)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This?344
3. (-5, 0), (2, 3)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This? 345
4. (4, -3), (-3, 4)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This?346
5. (0, 2), (-5, 7)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This? 347
6. (2, 2), (-1, -2)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This?348
7. (0, 0), (-4, 4)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This? 349
8. (3, 5), (-2, -7)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This?350
9. (6, -7), (-2, 8)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This? 351
10. (-4, 6), (5, -6)
-5 -4 -3 -2 -1 0 1 2 3 4 5 -1
-2
-3
-4
-5
1
2
3
4
5
76-6-7
-6
-7
7
6
8
10
9
8 109-10 -8-9
-8
-9
-10
y
x
Unit 6: Is There a Point to This?352
Practice
Use the list below to write the correct term for each definition on the line provided.
absolute value coordinate grid or plane distance graph (of a point)
horizontal negative numbers positive numbers
vertical x-axis y-axis
________________________ 1. parallel to or in the same plane of the horizon
________________________ 2. the length of a segment connecting two points
________________________ 3. at right angles to the horizon; straight up and down
________________________ 4. numbers less than zero
________________________ 5. a number’s distance from zero (0) on a number line
________________________ 6. numbers greater than zero
________________________ 7. the vertical number line on a rectangular coordinate system
________________________ 8. the point assigned to an ordered pair on a coordinate plane
________________________ 9. the horizontal number line on a rectangular coordinate system
________________________ 10. a two-dimensional network of horizontal and vertical lines that are parallel and evenly-spaced
Unit 6: Is There a Point to This? 353
Practice
Match each definition with the correct term. Write the letter on the line provided.
______ 1. a one-dimensional measure that is the measurable property of line segments
______ 2. the longest side of a right triangle; the side opposite the right angle
______ 3. the square of the hypotenuse (c) of a right triangle is equal to the sum of the square of the legs (a and b)
______ 4. the edge of a polygon
______ 5. a polygon with three sides
______ 6. a triangle with one right angle
______ 7. the result of adding numbers together
______ 8. in a right triangle, one of the two sides that form the right angle
______ 9. the result when a number is multiplied by itself or used as a factor twice
A. hypotenuse
B. leg
C. length (l)
D. Pythagorean theorem
E. right triangle
F. side
G. square (of a number)
H. sum
I. triangle
Unit 6: Is There a Point to This? 389
Practice
Use the list below to complete the following statements.
distance horizontal hypotenuse
line segment midpoint parallel
perpendicular slope vertical
1. The slant or of a line is defined as riserun .
2. A line that has no slope is called a line.
3. The between two points is the length of
the segment that connects the two points.
4. The is the segment in a right triangle that
is opposite the right angle.
5. Lines that are in the same plane and do not intersect are called
lines.
6. A line that has zero slope is a line.
7. The point that is located exactly half way between two endpoints of a
line segment is called the of a line
segment.
8. If two lines intersect to form right angles, they are
lines.
9. The figure that contains two defined endpoints and all the points in
between is called a .
Unit 6: Is There a Point to This?390
Practice
Match each definition with the correct term. Write the letter on the line provided.
______ 1. the square of the hypotenuse (c) of a right triangle is equal to the sum of the square of the legs (a and b), as shown in the equation c2 = a2 + b2
______ 2. two lines, two line segments, or two planes that intersect to form a right angle
______ 3. an angle whose measure is exactly 90°
______ 4. two lines in the same plane that are a constant distance apart; lines with equal slopes
______ 5. two numbers whose product is 1; also called multiplicative inverses
______ 6. to meet or cross at one point
______ 7. a way of expressing a relationship using variables or symbols that represent numbers
______ 8. the result of multiplying numbers together
A. formula
B. intersect
C. parallel lines
D. perpendicular ( )
E. product
F. Pythagorean theorem
G. reciprocals
H. right angle
- Unit 6 1.pdf
- Unit 6 2.pdf
