2:Here are four straight line equations.
A.3y=4x+5
B.4y=3x-1
C.4y+3x=7
D.4x+3y=2
Which one of the following statements is true? Explain by working
A. Lines 1 and 2 are perpendicular
B. Lines 1 and 4 are parallel
C. Lines 2 and 4 are perpendicular
D. Lines 2 and 3 are parallel
E. I don't know
Answers
Answer:
C. Lines 2 and 4 are perpendicular
Step-by-step explanation:
1. 3y = 4x + 5 => y = 4/3x + 5/3
2. 4y = 3x - 1 => y = 3/4x - 1/4
3. 4y + 3x = 7 => 4y = -3x + 7 => y = -3/4x + 7/4
4. 4x + 3y = 2 => 3y = -4x + 2 => y = -4/3x + 2/3
Comparing the above equations with y = mx+c,
we find that the
Slope of 1 (m1) = 4/3
Slope of 2 (m2) = 3/4
Slope of 3 (m3) = -3/4
Slope of 4 (m4) = -4/3.
We see that None of the slopes are equal to each other.
So, no lines are parellel.
Also, we see that m1*m3 = 4/3*-3/4 = -1
m2*m4 = 3/4*-4/3 = -1
We know, that the product of slopes of perpendicular lines = -1
Hence, lines 1 and 3 are perpendicular and lines 2 and 4 are perpendicular.
Note :- Opt. E. can also be justified as correct if it is true. :)