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Exercise 5.4

1. Find the slope of the following straight lines

(i) 5*y* − 3 = 0 (ii) 7*x* – 3/17 = 0

2. Find the slope of the line which is

(i) parallel to *y* = 0. 7*x* −11

(ii) perpendicular to the line *x* = −11

3. Check whether the given lines are parellel or perpendicular

(i) *x/*3 + *y/*4 + 1/7 = 0 and 2*x/*3 + *y/*2 + 1/10 = 0

(ii) 5*x* + 23*y* + 14 = 0 and 23*x* − 5*y* + 9 = 0

4. If the straight lines 12*y* = −( *p* + 3)*x* + 12 , 12*x* − 7*y* = 16 are perpendicular then find ‘*p*’.

5. Find the equation of a straight line passing through the point *P*(-5, 2) and parallel to the line joining the points *Q*(3, - 2) and *R*(-5, 4)

6. Find the equation of a line passing through (6,–2) and perpendicular to the line joining the points (6,7) and (2,–3).

7. *A*(-3, 0)* B*(10,* *-* *2)* *and* C*(12, 3)* *are the vertices of* *Δ*ABC *. Find the equation of the* *altitude through *A* and *B*.

8. Find the equation of the perpendicular bisector of the line joining the points *A*(-4, 2)* *and* B*(6,* *-* *4)* *.

9. Find the equation of a straight line through the intersection of lines 7*x* + 3*y* = 10 , 5*x* − 4*y* = 1 and parallel to the line 13*x* + 5*y* + 12 = 0

10. Find the equation of a straight line through the intersection of lines 5*x* − 6*y* = 2 , 3*x* + 2*y* = 10 and perpendicular to the line 4*x* − 7*y* + 13 = 0

11. Find the equation of a straight line joining the point of intersection of 3*x* + *y* + 2 = 0 and *x* − 2*y* − 4 = 0 to the point of intersection of 7*x* − 3*y* = −12 and 2*y* = *x* + 3

12. Find the equation of a straight line through the point of intersection of the lines 8*x* + 3*y* = 18 , 4*x* + 5*y* = 9 and bisecting the line segment joining the points (5,–4) and (–7,6).

1.(i) 0 (ii) undefined

2.(i) 0.7 (ii) undefined

3.(i) Parallel (ii) Perpendicular

4. 4

5. 3x + 4y + 7 = 0

6. 2x + 5y − 2 = 0

7. 2x + 5y + 6 = 0 , 5x + y − 48 = 0

8. 5x − 3y − 8 = 0

9. 13x + 5y − 18 = 0

10. 49x + 28y −156 = 0

11. 31x + 15y + 30 = 0

12. 4x + 13y − 9 = 0

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10th Mathematics : UNIT 5 : Coordinate Geometry : Exercise 5.4: General Form of a Straight Line | Problem Questions with Answer, Solution | Mathematics

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