EQUATION OF THE LINE WORKSHEET WITH ANSWER

(1)  Find the slope of the following straight lines

(i) 5y −3 = 0           Solution

(ii) 7 x - (3/17)  = 0          Solution

(2)  Find the slope of the line which is

(i) parallel to y = 0.7x −11          Solution

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

(3)  Check whether the given lines are parallel or perpendicular

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

Solution

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

Solution

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

Problem 1 :

A(-3, 0) B(10, -2) and C(12, 3) are the vertices of ΔABC. Find the equations of the altitudes through A, B and C in general form

Solution

Problem 2 :

Write the equation of the perpendicular bisector that goes through the line segment with end points of (9, 5) and (-7, 13).

Solution

Problem 3 :

Write the equation of the perpendicular bisector that goes through the line segment with end points of (10, -10) and B (2, 2).

Solution

Problem 4 :

Write the equation of the perpendicular bisector that goes through the line segment with end points of (-10, -8) and B (-14 , 8).

Solution

Problem 1 :

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

Solution

Problem 2 :

Write an equation of the line in y = mx + b form that is the perpendicular bisector of the line segment having endpoints of (1, 2) and (2, 4)

Solution

Problem 3 :

The straight line p has the equation 3x − 4y + 8 = 0. The straight line q is parallel to p and passes through the point with coordinates (8, 5).

a Find the equation of q in the form y = mx + c. The straight line r is perpendicular to p and passes through the point with coordinates (−4, 6).

b Find the equation of r in the form ax + by + c = 0, where a, b and c are integers.

c Find the coordinates of the point where lines q and r intersect.

Solution

Question 1 :

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

Solution

Question 2 :

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

Solution

Question 1 :

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

Solution

Question 2 :

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

Solution

Problem 1 :

Write the equation of the lines through the point (1, -1)

(i) parallel to x + 3y - 4 = 0

(ii) perpendicular to 3x + 4y = 6

Solution

Problem 2 :

If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal.

Solution

Problem 3 :

The line with equation 2x − 3y + 5 = 0 is perpendicular to the line with equation 3x + ky − 1 = 0. Find the value of the constant k.

Solution

Problem 4 :

The straight line l₁ passes through the points with coordinates (−3, 7) and (1, −5).

a) Find an equation of the line l₁ in the form ax + by + c = 0, where a, b and c are integers. The line l₂ is perpendicular to l₁ and passes through the point with coordinates (4, 6).

b) Find, in the form k√5, the distance from the origin of the point where l1 and l₂ intersect.

Solution

Problem 5 :

If AB is defined by the endpoints A(4, 2) and B(8, 6), write an equation of the line that is the perpendicular bisector of AB.

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