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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.


Solution

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

4 y equals negative 3 x minus 7 y equals fraction numerator negative 3 over denominator 4 end fraction x minus 7 over 4

Slope of this line =fraction numerator negative 3 over denominator 4 end fraction

28x - 21y + 50 = 0

21 y equals 28 x plus 50 y equals 28 over 21 x plus 50 over 21 y equals 4 over 3 x plus 50 over 21

Slope of this line = 4 over 3

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

(ii) x - 3y = 4

3y = x - 4

y =1 third x minus 4 over 3

Slope of this line =1 third

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 = fraction numerator negative 3 over denominator 2 end fraction x plus 5 over 2

Slope of this line = fraction numerator negative 3 over denominator 2 end fraction

x + 2y = 1

2y = -x + 1

y = fraction numerator negative 1 over denominator 2 end fraction x plus 1 half

Slope of this line = fraction numerator negative 1 over denominator 2 end fraction

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.

fraction numerator 2 minus 4 over denominator x minus 1 end fraction equals 2 fraction numerator negative 2 over denominator x minus 1 end fraction equals 2 x equals 0


Mathematics
Concise Mathematics
Standard X

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