Equation of a Straight Line — Part 2: Parallel and perpendicular lines, and applications: visual lesson, ICSE Class 10 Mathematics

Lesson

Equation of a Straight Line, Part 2

Slopes tell us when two lines are parallel and when they meet at right angles. With the mid-point and section formulae, they find the special lines of a triangle.

In this lesson you will

Test whether two lines are parallel or perpendicular using their slopes
Find the equation of a line parallel or perpendicular to a given line
Find unknown coefficients and the meeting point of two lines
Find the perpendicular bisector, median and altitude using the mid-point and section formulae

$y = 2x - 1$
$y = 2x + 4$
$y = -\dfrac{1}{2}x + 4$

Equal slopes: parallel. Slopes multiplying to $-1$: perpendicular.

Concept

What you will be able to do

Test lines for being parallel or perpendicular
Find a line parallel or perpendicular to a given line through a point
Find unknown coefficients and the meeting point of two lines
Find perpendicular bisectors, medians and altitudes

Concept

Parallel lines

Two non-vertical lines are parallel exactly when they have equal slopes:

equal slopes mean equal inclinations
parallel lines have different intercepts (equal intercepts would make them the same line)
any two vertical lines are parallel

m_1 = m_2

$y = \dfrac{1}{3}x + 2$
$y = \dfrac{1}{3}x - 1$

Same slope, different intercepts: parallel lines.

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