Welcome to your Coordinate Geometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. 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, 1/3) (3/8, 3/11) (5/3, 17/3) 2. If a graph of the function y = 3x² -5x - 7 is provided, the roots of the equation 3x² - 2x -5 = 0 are given by the points of intersection of the curve y = 3x² -5x - 7 and the line y = 3x - 2 y = -3x - 2 y = -7x - 2 y = 7x - 12 3. Which point is the reflection of the point (–7, 5) over the line y = –x? (7, 5) (7, -5) (-5, 7) (5, -7) 4. Which of the following lines is perpendicular to the line 5x + 2y = 6? 5y + 2x = -6 5y -2x = 6 5x - 2y = 6 2y - 5x = 6 5. The line y =3x + 1 intersects thecurve y = x² -2x + 7 at the points (2, 7) and (3, 10) (1, 4) and (2, 7) (-2, -5) and (1, 4) (-1, -2) and (3, 10) 6. Find the co-ordinates of a point on x-axis, which is at a distance of 5 units from the point (6, -3). (0,2) and ( 0,10). (2, 10) and (0, 0). (2, 0) and (10, 0). (2, 10) and (1, 0). 7. Find the gradients and the intercepts on the y- axis for 5x = 6y m = 1, c = -1/2 m = 5/6, c= 0 m = 1/6, c= -1 m = -1, c= -1 8. In a coordinate system, P = (2, 7) and Q = (2, –3). Which could be the coordinates of R if PQR is an isosceles triangle? I. (12, –3) II. (–6, –9) III. (–117, 2) II only II and III only I and III only I, II and III 9. Which of the following lines is not parallel to the line x - 2y = 5 ? 16x - 32y + 9 = 0 x + 2y - 3 = 0 2x - 4y - 1 = 0 x - 2y + 7 = 0 10. Which of the following points is located on the curve y =2x² - 3x - 5 ? (0, 5) (2, -1) (3,4) (1, 3) 11. The point (1, -2)is located on the graph of a linear function. If y increases by 3 units for each unit increase in x, the equation of the function is y - 3x = -5 y - 3x = 5 3y - x = 5 x -3y = 5 12. Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x + 2y + 4 = 0 y = x+2 y = 5/ 3x-2 3y = 5x-2 3y = 2x+5 13. Find the equation of the line passing through (2, -1) and parallel to the line 2x – y = 4. y = x+1 y = 2x-5 y = 5x-2 y = 2/ 5x-1 14. 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 15. Find the slope from the points -2/3 -3 9 2 16. 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 (-1, -2) (3, 6) (6, 12) (-2, -4) 17. Find the coordinate of the point which will divide the line joining the point (2, 4) and (7,9) internally in the ratio 1:2? (8/3 11/3) (11/3, 17/3) (3/8, 3/11) (5/3, 1/3) 18. 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 = x + 3 y = x -1 y = 1 + x 19. 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? 36 109 96 89 20. 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? 12 30 23 15 21. Determine the equation of a line that cuts the y-axis at -3 that is parallel to the line with equation 3x - 2y = -5 2y - 3x = 6 2y + 3x = -6 3x - 2y = 6 x - 3y = -9 22. The maximum value of y in the equation y = 1 + x - 4x² is 1 17/8 17/16 2 23. Find the equations of the straight lines joining (m, 2n) and (3m, n) 3nx +my - 8mn = 0 nx + 2my -5mn = 0 x+2ny -7mn = n nx - 3my - 10mn = 0 24. Find the slope of the line 2/3 1/2 1 2 25. The area of the triangle whose vertices are (a, a), (a + 1, a + 1) and (a + 2, a) is 1-2a a³ 1 2a 1 out of 25 Time is Up! Time's up