Rectangular Coordinates.docx

Rectangular coordinates, Straight Lines 1.

The inclination of the straight line passing through the point (-3,6) and the midpoint of the line joining the points (4,-5) and (-2,9) is (a) π 4

2.

(b)

(b) 1 3√34

(b) 600

(b) 5 2

5π 6

(c) (4,4)

(d) (4,1)

(e) (0,0)

(c) 35 3√34

(d)

35 2√34

(e) 35

(c) 450

(d) 300

(e) 1800

(c) 3 2

(d) 1 2

If the segment joining the points (a,b) and (c,d) subtends a right angle at the origin, then (a) ac - bd = 0 (c) ab + cd = 0

7.

(e)

The points (-2,-5), (2,-2), (8,a) are collinear, then the value of a is (a) -5 2

6.

3π 4

The angle between the lines 2x-y+3=0 and x+2y+3=0 is (a) 900

5.

(d)

Distance between the lines 5x+3y-7=0 and 15x+9y+14=0 is (a) 35 √34

4.

π 3

(c)

Three vertices of a parallelogram taken in order are (-1,-6), (2,-5) and (7,2). The fourth vertex is (a) (1,4) (b) (1,1)

3.

π 6

(b) ac + bd = 0 (d) ab - cd = 0

The centroid of the triangle formed by the points (1,a), (2,b) and (c2,-3) lies on the x-axis, then (a) a=3 (c) a+b=3

(b) b=3 (d) a-b=3

8.

The in centre of the triangle formed by (1,2), (3,4) and (2,3) is (a) (2,3)

9.

(b) (-2,3)

(c) (2,-3)

(d) None of these.

The line 3x+4y=24 cuts the axes at A and B. The area of (a) 48

(b) (b) 36

(c) 24

OAB is

(d) 64

10. The length of the perpendicular from the origin to the line x - y = 1 is 3 4 (a) 11 (b) 5 (c) 12 (d) -5 5 12 5 12 11. If the lines x-y-1=0 , 4x+3y=k and 2x – 3y+1 = 0 are concurrent, then K is (a) 1

(b) -1

(c) 25

(d) 5

(e) -20

12. The foot of the perpendicular from (-2,3) to the line 2x - y - 3 = 0 is (a) (-2,3)

(b) (2,1)

(c) (3,2)

(d) (1,2)

(e) (-3,-2)

13. The equation of the line passing through (a,b) and parallel to the line x + y = 1 is a b (a) x + y = 3 (b) x + y = 2 (c) x + y = 0 (d) x + y + 2 = 0 a b a b a b a b (e) x + y = 4 a b 14. The equation of the line passing through (-3,5) and perpendicular to the line through the points (1,0) and (-4,1) is (a) 5x + y + 10 = 0

(b) 5x - y + 20 = 0

(d) 5x + y + 20 = 0

(e) 5y - x - 10 = 0

15. The slope of the straight line 2x - 5y = 3 is 10 10

(c) 5x - y - 10 = 0

(a) 5 (b) -5 (c) 2 (d) -2 (e) 4 2 2 5 5 3 16. If y-intercept of the line 4x-ay=8 is thrice its x-intercept, then the value of a is equal to (a) 3 4

(b) 4 3

(c) -3 4

(d) -4 3

(e) -2 3

17. If the orthocenter, centroid, incentre and circumcentre coincide in triangle ABC and if the length of side AB is √75 units, then the length of the altitude of the triangle through the vertex A is (a) √ 3 units

(c) √15 2 18. A triangle with vertices (4,0) , (-1,-1) , (3,5) is (a) (b) (c) (d)

(b) 3 units

(d) 15 units 2

(e) √ 5 units 2

iscosceles and right angle d iscosceles but not right angled right angled but not isosceles neither right angled nor isosceles

19. Two sides of a parallelogram are along the lines x+y=3 & x-y+3=0. If its diagonals intersect at (2,4) then one of its vertex is (a) (2,1)

(b) (2,6)

(c) (3,5)

(d) (3,6)

20. If in a parallelogram ABDC, the coordinates of A,B and C are respectively (1,2) , (3,4) and (2,5) then the equation of the diagonal AD is: (a) 5x + 3y - 11= 0 (c) 3x - 5y + 7 = 0

(b) 5x - 3y + 1 = 0 (c) 3x + 5y - 13 = 0

Answer Key ( Rectangular coordinates, Straight lines) 1.

d

6.

b

11.

c

16.

d

2.

d

7.

c

12.

b

17.

d

3.

c

8.

a

13.

b

18.

a

4.

a

9.

c

14.

b

19.

d

5.

b

10.

c

15.

c

20.

b