Coordinate Geometry(Senior Class Maths Study by Topics Test) : GATE Academy

Welcome to your Coordinate Geometry(Senior Class Maths Study by Topics)

NAME

PHONE NUMBER

1. Find the slope of the line

2/3

1/2

2. Your new question!

3. The quadrants where abcissa and ordinate have different signs are?

1st & 2nd quadrant

2nd & 4th quadrant

2nd & 3rd quadrant

1st & 3rd quadrant

4. In which quadrant does the point (-3,4) lie?

3rd quadrant

4th quadrant

2nd quadrant

1st quadrant

Line M has a y-intercept of –4, and its slope must be an integer-multiple of 1/7.

Given that Line M passes below (4, –1) and above (5, –6), how many possible slopes could Line M have?

6. 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?

(11/3, 17/3)

(3/8, 3/11)

(8/3 11/3)

(5/3, 1/3)

In the figure, the point on segment JK that is four times as far from K as it is from J is:

(2,0)

(0, 2)

(-1, 3)

(-1/3, 7/3)

8. The line y =3x + 1 intersects the
curve y = x² -2x + 7 at the points

(-2, -5) and (1, 4)

(1, 4) and (2, 7)

(2, 7) and (3, 10)

(-1, -2) and (3, 10)

9. 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 = x + 3

y = x -1

y = 1 + x

y = 1 - x

10. Find the co-ordinates of a point on x-axis, which is at a distance of 5 units from the point (6, -3).

(2, 0) and (10, 0).

(2, 10) and (0, 0).

(0,2) and ( 0,10).

(2, 10) and (1, 0).

11. Find the equations of the straight lines joining (m, 2n) and (3m, n)

nx - 3my - 10mn = 0

x+2ny -7mn = n

3nx +my - 8mn = 0

nx + 2my -5mn = 0

12. Find the gradients and the intercepts on the y- axis for y+3= 0

m = 0, c = 3

m = 3, c = 0

m= 0, c= -3

m = -3, c= 0

13. Find the equation of the line whose slope is 2 and y intercept is - 3.

y = 2x-3

y = 3x-2

y = 2/ 3x-1

y = x+2

14. Which of the following pairs of graphs cannot be used to find the solution to the cubic equation x³ -3x² + 3x - 9 = 0 ?

y = x³ -3x² and y = 3x - 9

y = x³ and y = 3x² - 3x + 9

y = x² - 3x + 3and y = 9/x

y = x³ -3x² + 3x and y = 9

15.

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 and III only

I and III only

II only

I, II and III

16. 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?

17. Find the area of the triangle formed by the vertices (4, 5), (10, 12) and (-3, 2)

4.5

3.5

18. The equation of the line is

y = 1/2x -2

y = -2/3x + 2

-y = x+2

y = x+2

19. ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x-y plane. The equation of the straight line AD is x + y = 1. What is the equation of BC?

x + y = 1

x - y = -1

x - y = 1

x + y= -1

20. What is the slope of the line passing through the points J (-2, 3) and (2, 7)?

21. Which of the following lines is not parallel to the line x - 2y = 5 ?

x - 2y + 7 = 0

2x - 4y - 1 = 0

16x - 32y + 9 = 0

x + 2y - 3 = 0

22. 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).

(3/8, 3/11)

(5/3, 17/3)

(5/3, 1/3)

(8/3, 11/3)

23.

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?

109

24. Find the gradients and the intercepts on the y- axis for 5x = 6y

m = 1/6, c= -1

m = -1, c= -1

m = 5/6, c= 0

m = 1, c = -1/2

25. Which of the following points is located on the curve
y =2x² - 3x - 5 ?

(3,4)

(0, 5)

(2, -1)

(1, 3)

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