Question

(i) Is the line 3x + 4y + 7 = 0 perpendicular to the line 28x - 21y + 50 = 0 ?

(ii) Is the line x - 3y = 4 perpendicular to the line 3x - y = 7 ?

(iii) Is the line 3x + 2y = 5 parallel to the line x + 2y = 1 ?

(iv) Determine x so that the slope of the line through (1, 4) and (x, 2) is 2.

Answer 1

(i) 3x + 4y + 7 = 0

Slope of this line =

28x - 21y + 50 = 0

Slope of this line =

Since, product of slopes of the two lines = -1, the lines are perpendicular to each other.

(ii) x - 3y = 4

3y = x - 4

y =

Slope of this line =

3x - y = 7

y = 3x - 7

Slope of this line = 3

Product of slopes of the two lines = 1 -1

So, the lines are not perpendicular to each other.

(iii) 3x + 2y = 5

2y = -3x + 5

y =

Slope of this line =

x + 2y = 1

2y = -x + 1

y =

Slope of this line =

Product of slopes of the two lines = 3 -1

So, the lines are not perpendicular to each other.

(iv) Given, the slope of the line through (1, 4) and (x, 2) is 2.