2009-2010
1. In the xy–plane, the equation of line l is y = 2x + 5. If line m is the reflection of line l in the x–axis, what is the equation of line m ?
(A) y = –2x – 5 (B) y = –2x + 5 (C) y = 2x – 5 (D) y =
2 1x – 5
(E) y = 2
1x + 5
2. In the xy–plane, line l passes through the origin and is perpendicu1ar to the line
k y
4x where k is a constant. If the two lines intersect at the point (t, t + 1), what is the value of t?
(A) 3 4 (B) 4
5
(C) 4 3
(D) 4 5 (E)
3 4
3. In the figure above, what is the slope of line ℓ ?
(A) (B) (C) (D) (E)
4. In the coordinate plane, the points F and H lie on a circle with center P.
What are the coordinates of point P ? (A
(B) (C) (D) (E)
COORDINATES GEOMETRY
2009-2010 2009-2010
5. Which of the following is the graph of a linear function with a negative slope and a positive y–intercept?
(A)
(B)
(C)
(D)
(E)
6. In the figure above, the scale on the x–axis is different from the scale on the y–axis. If the area of ∆ABC is 18, what is the value of k?
(A) 10 3 (B) 4
3
(C) 5 6 (D) 2 3 (E) 3
7. In the xy–plane, the center of a circle has coordinates (3, –7). If one endpoint of a diameter of the circle is (–2, –7), what are the coordinates of the other endpoint of this diameter?
(A) (–7, –7) (B) (–2,–2) (C) (3, –2) (D) (8, –2) (E) (8, –7)
COORDINATES GEOMETRY
2009-2010 2009-2010
8. In the figure above, RS = ST and the coordinates of S are (k, 3).
What is the value of k?
(A) –3 (B) 3 (C) 0 (D) 3 (E) 3
9. If the areas of the two rectangles in the figure above are equal, which of the following could be the coordinates of point P ?
(A) (−5, −3) (B) (−5, 3) (C) (5, − 5) (D) (5, − 3) (E) (5, 3)
10. What is an equation of line in the figure above?
(A) y=
(B) y=
(C) y=
(D) y=
(E) y=
11. In the xy -plane, an equation of line ℓ is y=3x−1. If line m is the reflection of line ℓ in the y -axis, what is an equation of line m ? (A) y= −3x−1
(B) y= −3x+1 (C) y=3x+1 (D) y=
(E) y=
COORDINATES GEOMETRY
2009-2010 2009-2010
12. In the xy-coordinate plane, the graph of y= intersects line ℓ at (p, 5) and (t, -7). What is the least possible value of the slope of ℓ?
(A) 6 (B) 2 (C) -2 (D) -6 (E) -10
13. In the xy–coordinate system above, which of the following line segments has a slope of –1?
(A) OA (B) OB (C) OC (D) OD (E) DC
14. In the figure above, line l passes through the origin. What is the value of h
k ?
(A) 3 (B) 2 (C) 2
3 (D) 2
3 (E) –3
COORDINATES GEOMETRY
2009-2010 2009-2010
15. The figure above shows the graph of the line y = mx + b, where m and b are constants. Which of the following best represents the graph of the line y = –3mx + b?
(A)
(B)
(C)
(D)
(E)
16. The figure above shows the graph of the line y = ax + b, where a and b are constants.
Which of the following best represents the graph of the line y = 2ax + b?
(A)
(B)
(C)
(D)
(E)
COORDINATES GEOMETRY
2009-2010 2009-2010
17. Rectangle ABCD lies in the xy–coordinate plane so that its sides are not parallel to the axes. What is the product of the slopes of all four sides of rectangle ABCD?
(A)–2 (B) –1 (C) 0 (D) 1 (E) 2
18. In the xy–plane above, points Q and S are the centers of the circles, which are tangent to the x–axis. What is the slope of line QS (not shown)?
(A) 8 1 (B) 4 1 (C) 2 1 (D) 8
7 (E) 1
19. Which of the lettered points in the figure above has coordinates (x, y) such that
y 3
x ?
(A) A (B) B (C) C (D) D (E) E
20. In the figure above, if the legs of
triangle ABC are parallel to the axes, which of the following could be the lengths of the sides of triangle ABC?
(A) 2, 5, and 29 (B) 2, 5,and 7 (C) 3, 3, and 3 2 (D) 3, 4,and 5
COORDINATES GEOMETRY
2009-2010 2009-2010
21. In the figure above, the slope of line ℓ is . What is the value of k ?
(A) 3 (B) (C) (D) 2 (E)
22. If the areas of the two rectangles in the figure above are equal, which of the following could be the coordinates of point R ?
(A) (B) (C) (D) (E)
COORDINATES GEOMETRY
2009-2010
1. In the figure above, line ℓ (not shown) is perpendicular to and bisects . Which of the following points lies on line ℓ?
(A) (B) (C) (D) (E)
2. In the figure above, the coordinates of P are (10 -2a, 0) - and the coordinates of Q are (10, a). A point in square ORST is to be chosen at random. If the probability that the point will be in the shaded triangle is what is the value of a?
(A) (B) (C) 2 (D) 2 (E) 5
3. Point P is the point with the greatest y-coordinate on the semicircle shown above.
What is the x-coordinate of point Q ? (A) -3.5
(B) -3 (C) -2.5 (D)-2 (E)-1.5
4. Point S is the point with the greatest y -coordinate on the semicircle shown above.
What is the x –coordinate of point R ? (A) −5.5
(B) −4 (C) −3.5 (D) −3 (E) −2.5
COORDINATES GEOMETRY
2009-2010 2009-2010
5. What is an equation of the line parallel to the x –axis and two units above the x -axis?
(A) x = −2 (B) x = 2 (C) y = −2 (D) y = 0 (E) y = 2
6. Which of the lettered points in the figure above has coordinates (x,y) such that
y=5?
(A) A (B) B (C) C (D) D (E) E
7. In the figure above, if line ℓ has a slope of -2, what is the y-intercept of ℓ?
(A) 7 (B) 8 (C) 9 (D) 10 (E) 12
8. If x is the coordinate of the indicated point on the number line above, which of the lettered points has coordinate -2x ? (A) A
(B) B (C) C (D) D (E) E
COORDINATES GEOMETRY
2009-2010 2009-2010
Questions 9-10 refer to the following figure and information.
The grid above represents equally spaced streets in a town that has no one-way streets.
F marks the corner where a firehouse is located. Points W, X, Y, and Z represent the locations of some other buildings. The fire company defines a building’s m-distance as the minimum number of blocks that a fire truck must travel from the firehouse to reach the building. For example, the building at X is an m-distance of 2, and the building at Y is an m-distance of from the firehouse.
9. What is the m-distance of the building at W from the firehouse?
(A) 2 (B) 2 (C) 3 (D) 3 (E) 4
10. What is the total number of different routes that a fire truck can travel the m-distance from F to Z ?
(A) Six (B) Five (C) Four (D) Three (E) Two
11. All of the buildings in the town that are an m-distance of 3 from the firehouse must lie on a
(A) circle (B) square
(C) right isosceles triangle (D) pair of intersecting lines (E) line
12. In the figure above, line ℓ intersects the x-axis at x = -2 and the y-axis at y = -3. If line m (not shown) passes through the origin and is perpendicular to line ℓ, what is the slope of line m ?
COORDINATES GEOMETRY
2009-2010 2009-2010
13. In the xy–coordinate plane, the distance between point B(10, 18) and point A(x, 3) is 17. What is one possible value of x?
14. In a rectangular coordinate system, the center of a circle has coordinates (5, 12), and the circle touches the x–axis at one point only. What is the radius of the circle?
15. In the figure above, PQRS is a rectangle, and points Q and. R lie on the graph of y
= ax2, where a is a constant. If the perimeter of PQRS is 10, what is the value of a?
16. In the figure above, ABCD is a rectangle. Points A and C lie on the graph of y = px3, where p is a constant.
If the area of ABCD is 4, what is the value of p?
17. Point P lies on the line with equation y – 4 = 3(x – 2). If the x–coordinate of P is 4, what is the y–coordinate of P ?
COORDINATES GEOMETRY
2009-2010 2009-2010
18. Line m (not shown) passes through O and intersects AB between A and B.
What is one possible value of the slope of line m?
19. In the xy-plane above, the area of ∆OST is 8. What is the value of a ?
20. In the xy -coordinate plane, the distance between points P(10,y) and Q(70, 14) is 61.
What is one possible value of y ?
21. In the xy -coordinate plane above, AC = 3, BC = 5, and is perpendicular to . If the coordinates of point A are (1, 0), what is the y -intercept of line ℓ ?