Is the line through (-2, 3) and (4, 1) perpendicular to the line 3x = y + 1? Does the line 3x = y + 1 bisect the join of (-2, 3) and (4, 1)?
Straight Line Eq
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Question

Is the line through (-2, 3) and (4, 1) perpendicular to the line 3x = y + 1? Does the line 3x = y + 1 bisect the join of (-2, 3) and (4, 1)?

KnowledgeBoat · Accepted Answer

Equation of line through (-2, 3) and (4, 1) can be given by two-point form i.e., Putting values in above formula we get, Comparing the above equation with y = mx + c we get, slope = m₁ = The other equation is 3x = y + 1 or y = 3x - 1, comparing this with y = mx + c we get, slope = m₂ = 3. Product of slopes, Since, the product of slopes is -1 hence, the lines are perpendicular to each other. Mid-point of (-2, 3) and (4, 1) can be given by mid-point formula i.e., = (1, 2). Line 3x = y + 1 bisects the line joining (-2, 3) and (4, 1) if the mid-point i.e., (1, 2) satisfies the equation. Putting (1, 2) in 3x = y + 1. L.H.S. = 3x = 3(1) = 3. R.H.S. = y + 1 = 2 + 1 = 3. Since, L.H.S. = R.H.S. hence, (1, 2) satisfies 3x = y + 1. Hence, the line 3x = y + 1 is perpendicular to the line joining (-2, 3) and (4, 1) and also bisects it.

Mathematics

Is the line through (-2, 3) and (4, 1) perpendicular to the line 3x = y + 1? Does the line 3x = y + 1 bisect the join of (-2, 3) and (4, 1)?

Straight Line Eq

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