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Equations of Lines and Circles, and Segment Partition

Quiz by Joe Mahoney

High School
Geometry
New York State Next Generation Standards

Feel free to use or edit the questions

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Measures 2 skills from
High School
Geometry
New York State Next Generation Standards
GEO-G.GPE.B
Use coordinates to prove simple geometric theorems algebraically.
GEO-G.GPE.A
Translate between the geometric description and the equation of a conic section.

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Q 1/60
Score 0
What is the equation of a line that is parallel to the line whose equation is y = x + 2?
300
2x + y = −2
y − 2x = 3
y − x = −1
x + y = 5

60 questions

Q.What is the equation of a line that is parallel to the line whose equation is y = x + 2?
1
300 sec
GEO-G.GPE.B
Q.What is the slope of a line perpendicular to the line whose equation is y = −23\frac{2}{3}x − 5?
2
300 sec
GEO-G.GPE.B
Q.What is an equation of the line that passes through the point (6,−5) and is parallel to the line whose equation is 2x − 3y = 11?
3
300 sec
GEO-G.GPE.B
Q.The lines represented by the equations y + 12\frac{1}{2}x = 4 and 3x + 6y = 12 are
4
300 sec
GEO-G.GPE.B
Q.What is the slope of a line perpendicular to the line whose equation is 2y = −6x + 8?
5
300 sec
GEO-G.GPE.B
Q.The equation of a circle is x2^{2} + (y − 7)2^{2} = 16. What are the center and radius of the circle?
6
300 sec
GEO-G.GPE.A
Q.Which equation represents circle K shown in the graph?
7
300 sec
GEO-G.GPE.A
Q.What are the center and the radius of the circle whose equation is (x - 3)2^{2} + (y + 3)2^{2} = 36
8
300 sec
GEO-G.GPE.A
Q.What is an equation of the circle with a radius of 5 and center at (1,−4)?
9
300 sec
GEO-G.GPE.A
Q.Which equation represents the line parallel to the line whose equation is 4x + 2y = 14 and passing through the point (2,2)?
10
300 sec
GEO-G.GPE.B
Q.Which equation represents the perpendicular bisector of AB whose endpoints are A(8,2) and B(0,6)?
11
300 sec
GEO-G.GPE.B
Q.The equation of a circle with its center at (-3,5) and a radius of 4 is
12
300 sec
GEO-G.GPE.A
Q.What is an equation of the circle shown in the graph below?
13
300 sec
GEO-G.GPE.A
Q.Which equation represents a line that is parallel to the line whose equation is y = 32\frac{3}{2}x + 3 and passes through the point (1,2)?
14
300 sec
GEO-G.GPE.B
Q.Which equation represents the line that is perpendicular to 2y = x + 2 and passes through the point (4,3)?
15
300 sec
GEO-G.GPE.B
Q.What is an equation of the circle with center (-5,4) and a radius of 7?
16
300 sec
GEO-G.GPE.A
Q.Which is an equation of the graphed circle?
17
300 sec
GEO-G.GPE.A
Q.The lines represented by the equations 3y + 6 = 2x and 2y - 3x = 6 are
18
300 sec
GEO-G.GPE.B
Q.Which graph represents a circle whose equation is x2^{2} + (y - 2)2^{2} = 4
19
300 sec
GEO-G.GPE.A
Q.Triangle ABC has vertices with coordinates A(0,0), B(6,8), and C(8,4). Which equation represents the perpendicular bisector of BC?
20
300 sec
GEO-G.GPE.B
Q.A circle has the equation (x - 3)2^{2} + (y + 4)2^{2} = 10. The coordinates of the center of the circle and the length of the circle’s radius are
21
300 sec
GEO-G.GPE.A
Q.What is an equation of the line that passes through (-9,12) and is perpendicular to the line whose equation is y = 13\frac{1}{3}x + 6?
22
300 sec
GEO-G.GPE.A
Q.The equation of a circle is x2^{2} + y 2^{2} + 6y = 7. What are the coordinates of the center and the length of the radius of the circle?
23
300 sec
GEO-G.GPE.A
Q.If x2^{2} + y 2^{2} + 4x - 6y - 12 = 0 is the equation of a circle, the length of the radius is
24
300 sec
GEO-G.GPE.A
Q.What are the coordinates of the center and length of the radius of the circle whose equation is x2^{2} + y 2^{2} + 6x - 4y = 23
25
300 sec
GEO-G.GPE.A
Q.Kevin’s work for deriving the equation of a circle is shown. In which step did Kevin make an error?
26
300 sec
GEO-G.GPE.A
Q.What are the coordinates of the center and the length of the radius of the circle whose equation is x2^{2} + y 2^{2} - 6y + 1 = 0?
27
300 sec
GEO-G.GPE.A
Q.What are the coordinates of the center and the length of the radius of the circle represented by the equation x2^{2} + y 2^{2} - 4x + 8y + 11 = 0
28
300 sec
GEO-G.GPE.A
Q.The equation of a circle is x2^{2} + y 2^{2} - 12y + 20 = 0. What are the coordinates of the center and the length of the radius of the circle?
29
300 sec
GEO-G.GPE.A
Q.The equation of a circle is x2^{2} + y 2^{2} - 6x + 2y = 6. What are the coordinates of the center and the length of the radius of the circle?
30
300 sec
GEO-G.GPE.A
Q.What is an equation of circle O shown in the graph below?
31
300 sec
GEO-G.GPE.A
Q.An equation of circle O is x2^{2} + y 2^{2} + 4x - 8y = -16. The statement that best describes circle O is the
32
300 sec
GEO-G.GPE.A
Q.What is an equation of a circle whose center is (1,4) and diameter is 10?
33
300 sec
GEO-G.GPE.A
Q.The equation of a circle is x2^{2} + y 2^{2} + 8x - 12y = 144. What are the coordinates of the center and the length of the radius of the circle?
34
300 sec
GEO-G.GPE.A
Q.What is an equation of a circle whose center is at (2, 4) and is tangent to the line x = -2?
35
300 sec
GEO-G.GPE.A
Q.Which equation represents a line that is perpendicular to the line represented by 2x - y = 7?
36
300 sec
GEO-G.GPE.B
Q.The coordinates of the endpoints of AB are A(-6, -5) and B(4,0). Point P is on AB. Determine and state the coordinates of point P, such that AP:PB is 2:3. [Be sure to write your answer in the form (x, y)]
37
300 sec
Q.Point Q is on MN such that MQ:QN = 2:3. If M has coordinates (3,5) and N has coordinates (8, -5), the coordinates of Q are
38
300 sec
GEO-G.GPE.B
Q.Given MN shown, with M(-6,1) and N(3,-5), what is an equation of the line that passes through point P(6,1) and is parallel to MN?
39
300 sec
GEO-G.GPE.B
Q.The endpoints of DEF are D(1,4) and F(16,14). Determine and state the coordinates of point E, if DE:EF = 2:3. [Be sure to write your answer in the form (x, y)]
40
300 sec
GEO-G.GPE.B
Q.An equation of a line perpendicular to the line represented by the equation y= -12\frac{1}{2}x - 5 and passing through (6, 4) is
41
300 sec
GEO-G.GPE.B
Q.Directed line segment PT has endpoints whose coordinates are P(-2,1) and T(4,7). Determine the coordinates of point J, on PT, that divides the segment in the ratio 2 to 1. [Be sure to write your answer in the form (x, y)]
42
300 sec
GEO-G.GPE.B
Q.Line segment NY has endpoints N(-11,5) and Y(5, -7). What is the equation of the perpendicular bisector of NY ?
43
300 sec
GEO-G.GPE.B
Q.Point P is on segment AB such that AP:PB is 4:5. If A has coordinates (4,2), and B has coordinates (22,2), determine and state the coordinates of P. [Be sure to write your answer in the form (x, y)]
44
300 sec
GEO-G.GPE.B
Q.The diagonals of rhombus TEAM intersect at P(2,1). If the equation of the line that contains diagonal TA is y = -x + 3, what is the equation of a line that contains diagonal EM ?
45
300 sec
GEO-G.GPE.B
Q.Point P is on the directed line segment from point X(-6, -2) to point Y(6,7) and divides the segment in the ratio 1:5. What are the coordinates of point P?
46
300 sec
GEO-G.GPE.B
Q.Line segment RW has endpoints R(-4,5) and W(6,20). Point P is on RW such that RP:PW is 2:3. What are the coordinates of point P?
47
300 sec
GEO-G.GPE.B
Q.What is an equation of a line that is perpendicular to the line whose equation is 2y = 3x - 10 and passes through (-6,1)?
48
300 sec
Q.The coordinates of the endpoints of AB are A(-8, -2) and B(16,6). Point P is on AB. What are the coordinates of point P, such that AP:PB is 3:5?
49
300 sec
GEO-G.GPE.B
Q.What is an equation of the perpendicular bisector of the line segment shown in the diagram?
50
300 sec
GEO-G.GPE.B
Q.In the diagram, AC has endpoints with coordinates A(-5,2) and C(4, -10). If B is a point on AC and AB:BC = 1:2, what are the coordinates of B?
51
300 sec
GEO-G.GPE.B
Q.What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x - 6y = 15?
52
300 sec
GEO-G.GPE.B
Q.What is an equation of the line that passes through the point (6,8) and is perpendicular to a line with equation y= 32\frac{3}{2}x + 5?
53
300 sec
GEO-G.GPE.B
Q.Directed line segment DE has endpoints D(-4, -2) and E(1,8). Point F divides DE such that DF:FE is 2:3. What are the coordinates of F?
54
300 sec
GEO-G.GPE.B
Q.Which equation represents a line that is perpendicular to the line represented by y = 23\frac{2}{3}x + 1?
55
300 sec
GEO-G.GPE.B
Q.The coordinates of the endpoints of directed line segment ABC are A(-8, 7) and C(7, -13). If AB:BC = 3:2, the coordinates of B are
56
300 sec
GEO-G.GPE.B
Q.Point M divides AB so that AM:MB = 1:2. If A has coordinates (-1, -3) and B has coordinates (8,9), the coordinates of M are
57
300 sec
GEO-G.GPE.B
Q.Which equation represents a line parallel to the line whose equation is -2x + 3y = -4 and passes through the point (1,3)?
58
300 sec
GEO-G.GPE.B
Q.What are the coordinates of point C on the directed segment from A(-8,4) to B(10,-2) that partitions the segment such that AC:CB is 2:1?
59
300 sec
GEO-G.GPE.B
Q.The endpoints of directed line segment PQ have coordinates of P(-7, -5) and Q(5,3). What are the coordinates of point A, on PQ, that divide PQ into a ratio of 1:3?
60
300 sec
GEO-G.GPE.B

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