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Unit 1 Test Corrections 35 Questions...
Transcript of Unit 1 Test Corrections 35 Questions...
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Test Corrections for Unit 1 Test
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1. Trapezoid ABCD has coordinates A(0, 9),
B(12, 9), C(8, 4), and D(0, 4).
a) Using coordinate geometry, show that−−−AD
is not parallel to−−−BC.
b) Find the area of trapezoid ABCD.
c) Find the perimeter of ABCD to the
nearest integer.
d) Find m∠ABC to the nearest degree.
2. Point P has coordinates (−12, 5). What is itsdistance from the origin?
3. Find an equation of the line passing through
the point (6, 5) and perpendicular to the line
whose equation is 2y + 3x = 6.
4. Square ABCD has vertices A(−2,−3), B(4,−1),C(2, 5), and D(−4, 3). What is the length of aside of the square?
A. 2√5 B. 2
√10 C. 4
√5 D. 10
√2
5. In the diagram below, quadrilateral ABCD
has vertices A(−5, 1), B(6,−1), C(3, 5), andD(−2, 7).
What are the coordinates of the midpoint of
diagonal−−−AC?
A. (−1, 3) B. (1, 3)
C. (1, 4) D. (2, 3)
6. Find the distance between the points (−1, 5)and (−7, 3).
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7. Line ` passes through the point (5, 3) and is
parallel to line k whose equation is 5x + y = 6.
An equation of line ` is
A. y =1
5x + 2 B. y = −5x + 28
C. y =1
5x − 2 D. y = −5x − 28
8. In the coordinate plane, the points (2, 2) and
(2, 12) are the endpoints of a diameter of a
circle. What is the length of the radius of the
circle?
A. 5 B. 6 C. 7 D. 10
9. What is an equation of the line that passes
through the point (7, 3) and is parallel to the
line 4x + 2y = 10?
A. y =1
2x − 1
2B. y = −1
2x +
13
2
C. y = 2x − 11 D. y = −2x + 17
10. What is the length of the line segment joining
the points (−3,−4) and (2,−5)?
11. In parallelogram ABCD, the coordinates of A
are (4, 3) and the coordinates of the midpoint
of diagonal−−−AC are (2, 5). What are the
coordinates of C ?
12. The coordinates of the endpoints of the
diameter of a circle are (3, 7) and (−5, 3).Find the coordinates of the center of the circle.
13. The coordinates of A and B are (2a, 4b) and
(8a, 6b), respectively. Express in terms of a
and b, the coordinates of the midpoint of−−−AB.
14. Trapezoid ABCD has coordinates A(−6, 0),B(17, 0), C(2, 8), and D(0, 8). Find the
a) area of trapezoid ABCD
b) perimeter of trapezoid ABCD
c) measure of ∠B to the nearest degree
15. The midpoint of−−−AB is M, the coordinates of
A are (a, b), and the coordinates of B are
(a + 4, 5b). What are the coordinates of M?
A. (2, 2b) B. (a + 2, 3b)
C. (2a + 4, 6b) D.
(
a + 4
2,
5b
2
)
16. Triangle HKL has vertices H(−7, 2), K(3,−4),and L(5, 4). The midpoint of
−−−HL is M and the
midpoint of−−−LK is N.
Determine and state the coordinates of
points M and N.
Justify the statement:−−−−MN is parallel to
−−−−HK.
[The use of the set of axes below is optional.]
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17. The coordinates of the vertices of ^ABC are
A(−4, 1), B(4, 9), C(9,−2). Point M(1, 6) lieson−−−AB.
a) Show by means of coordinate geometry
that−−−−CM ⊥ −−−AB.
b) Find, to the nearest degree, the measure
of angle A.
18. The graph of the equation y = 13x + 2 is
perpendicular to the graph of the equation
A. y =1
3x + 5 B. 3y = x + 2
C. y = 3x + 5 D. y = −3x + 2
19. Which point is farthest from the origin?
A. (0,−5) B. (6, 0)
C. (3, 4) D. (4, 2)
20. Triangle ABC has vertices A(−2, 1), B(5, 5),and C(−1,−7).
a) Show that ^ABC is isosceles.
b) Find the length of the altitude drawn
from A to−−−BC.
c) Using the results obtained in parts a
and b, find, to the nearest degree, the
measure of a base angle of this triangle.
21. Which equation represents a line parallel to the
line whose equation is 2y = 3x + 6?
A. 3y = 2x + 6 B. 2y = −3x + 6
C. y =2
3x + 1 D. y =
3
2x − 4
22. Which equation represents a line that is parallel
to the line whose equation is 2x + 3y = 12?
A. 6y − 4x = 2 B. 6y + 4x = 2
C. 4x − 6y = 2 D. 6x + 4y = −2
23. Segment AB is the diameter of a circle whose
center is the point (2, 5). If the coordinates of
A are (1, 3), find the coordinates of B.
24. Points A(5, 3) and B(7, 6) lie on←→AB. Points
C(6, 4) and D(9, 0) lie on←→CD. Which
statement is true?
A.←→AB ‖ ←→CD
B.←→AB ⊥ ←→CD
C.←→AB and
←→CD are the same line.
D.←→AB and
←→CD intersect, but are not
perpendicular.
25. Which equation represents a line that is parallel
to the line whose equation is 3x − 2y = 7?
A. y = −32x + 5 B. y = −2
3x + 4
C. y =3
2x − 5 D. y = 2
3x − 4
26. Which line is perpendicular to the line whose
equation is 5y + 6 = −3x?
A. y = −53x + 7 B. y =
5
3x + 7
C. y = −35x + 7 D. y =
3
5x + 7
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27. Write an equation of the perpendicular bisector
of the line segment whose endpoints are
(−1, 1) and (7,−5). [The use of the gridbelow is optional.]
28. Which equation represents the line that passes
through the point (0, 1) and is parallel to the
line whose equation is 3x + y = 5?
A. 3x + y = 3 B. 3x + y = 1
C. 3x + y = 0 D. 3x + y = −1
29. Write an equation of the line that passes
through the point (6,−5) and is parallel to theline whose equation is 2x − 3y = 11.
30. What is an equation of the line that passes
through the point (3,−1) and has a slope of 2?
A. y = 2x + 5 B. y = 2x − 1
C. y = 2x − 4 D. y = 2x − 7
31. What is the equation of the line that is
perpendicular to the line y − 2x = 4 and passesthrough point (2, 4)?
A. y =1
2x + 4 B. y = −1
2x + 5
C. y =1
2x + 5 D. y = −2x + 5
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