Straight Lines — Practice

Question 1

Find the slope of the line passing through (2, 3) and (5, 9). Is the line rising or falling?

Accepted Answer

m = (9−3)/(5−2) = 6/3 = 2. Since m = 2 > 0, the line is RISING (left to right).

Question 2

Find the perpendicular distance from the point (3, −4) to the line 3x − 4y + 5 = 0.

Accepted Answer

Here A=3, B=−4, C=5, x₁=3, y₁=−4. d = |3(3)+(−4)(−4)+5| / √(3²+(−4)²) = |9+16+5| / √(9+16) = |30| / √25 = 30/5 = 6.

Question 3

Find the acute angle between the lines 2x + 3y − 5 = 0 and 3x − 2y + 7 = 0. What do you conclude about these lines?

Accepted Answer

Line 1: slope m₁ = −A/B = −2/3. Line 2: slope m₂ = −3/(−2) = 3/2. Product m₁m₂ = (−2/3)(3/2) = −1. Since m₁m₂ = −1, the lines are PERPENDICULAR (angle = 90°). Verification using formula: tan θ = |(m₁−m₂)/(1+m₁m₂)| = |(−2/3−3/2)/(1+(−1))| = |(−13/6)/0| → undefined → θ = 90°.

Practice — Straight Lines

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