Welcome to your Coordinate Geometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. The area of the triangle whose vertices are (a, a), (a + 1, a + 1) and (a + 2, a) is 2a a³ 1 1-2a 2. The points of intersection of the graphs of y = x² + 2 and y = 2x + 5 when drawn on the same set of axes are (-1, 11) and (3, 3) (1, 0) and (-3, 0) (3, 0) and (-1, 0) (-1, 3) and (3, 11) 3. In the x-y plane, point (p, q) is a lattice point if both p and q are integers. Circle C has a center at (–2, 1) and a radius of 6. Some points, such as the center (–2, 1), are inside the circle, but a point such as (4, 1) is on the circle but not in the circle. How many lattice points are in circle C? 89 109 36 96 4. The quadrants where abcissa and ordinate have different signs are? 1st & 3rd quadrant 2nd & 4th quadrant 2nd & 3rd quadrant 1st & 2nd quadrant 5. The graph of the function 2y = x² - x - 6 intersects the y axis at the point (0, -6) (-2, 0) (0, -3) (2, -3) 6. Which of the following pairs of graphs cannot be used to find the solution to the cubic equation x³ -3x² + 3x - 9 = 0 ? y = x² - 3x + 3and y = 9/x y = x³ and y = 3x² - 3x + 9 y = x³ -3x² and y = 3x - 9 y = x³ -3x² + 3x and y = 9 7. Point W = (5, 3). Circle J has a center at point W and radius of r = 5. This circle intersects the y-axis at one intercept and the x-axis at two intercepts. What is the area of the triangle formed by these three intercepts? 15 23 30 12 8. Your new question! 9. Find the gradients and the intercepts on the y- axis for 3y-2x+5 = 0 m = 1, c = -1 m = 2/3, c=-5/3 m = 1/3, c = 5/3 m= 3, c = -5 10. The intercept of the line y = 3x on the x-axis is 1/3 1 0 3 11. Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x + 2y + 4 = 0 3y = 5x-2 y = 5/ 3x-2 3y = 2x+5 y = x+2 12. In the figure, the point on segment JK that is four times as far from K as it is from J is: (-1/3, 7/3) (0, 2) (2,0) (-1, 3) 13. Which point is the reflection of the point (–7, 5) over the line y = –x? (7, -5) (-5, 7) (5, -7) (7, 5) 14. Find the co-ordinates of the point of intersection of the medians of triangle MNO; given M = (-2, 3), N = (6, 7), O = (4, 1). (8/3, 11/3) (5/3, 17/3) (5/3, 1/3) (3/8, 3/11) 15. Find the gradients and the intercepts on the y- axis for y+3= 0 m = -3, c= 0 m = 0, c = 3 m = 3, c = 0 m= 0, c= -3 16. Determine the equation of a line that cuts the y-axis at -3 that is parallel to the line with equation 3x - 2y = -5 x - 3y = -9 2y - 3x = 6 3x - 2y = 6 2y + 3x = -6 17. The points of intersection between a straight line and the curve y = -x² + x + 2 give the roots of the equation x² - 2x - 1 = 0. The equation of the line is y = 1 - x y = 1 + x y = x -1 y = x + 3 18. The points of intersection of the curve y = -2x² - x + 3 with the coordinate axes are (1, 0), (-3/2, 0) and (0,3) (3/2, 0), (1, 0) and (0, -3) (0,0), (1, 3/2) and (0, -3) (-1, 0), (3/2, 0) and (0,3) 19. In which quadrant does the point (-3,4) lie? 4th quadrant 3rd quadrant 2nd quadrant 1st quadrant 20. Line Q has the equation 5y – 3x = 45. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.) 36 33 25 41 21. Find the equation of the line passing through (2, -1) and parallel to the line 2x – y = 4. y = 5x-2 y = 2x-5 y = x+1 y = 2/ 5x-1 22. A straight line y = ax intersects the parabola y = x² -5x + 6 at points P(1,2) and Q(m,n). The values of m and n are (3, 6) (6, 12) (-1, -2) (-2, -4) 23. Find the area of the triangle formed by the vertices (4, 5), (10, 12) and (-3, 2) 4.5 3 4 3.5 24. What is the slope of the line passing through the points J (-2, 3) and (2, 7)? 3 4 1 2 25. The maximum value of y in the equation y = 1 + x - 4x² is 17/16 1 17/8 2 1 out of 25 Time is Up! Time's up