Perpendicular — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
Slopes multiply to -1 — negative reciprocals.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Reciprocal — The flip of a fraction. The reciprocal of 35 is 53.
- Slope — How much y changes for each 1 that x increases.
What uses it later
This idea is needed for:
- Height — The perpendicular distance from the base to the opposite corner.
Practise this idea
14 questions in the course bank use Perpendicular, in Length and Area in 2-D Figures, Measurement, Slope & the Forms of a Line, Quadrilaterals & Polygon Properties, Circle Angles, Arcs & Chords, Coordinate Geometry Proofs. The first 8 are below; the rest are in those units.
Problem 1
Find the area of a parallelogram with base 12 and height 5.
Worked answer
60
12 × 5 = 60
Problem 2
Find the area of a triangle with base 14 and perpendicular height 9.
Worked answer
63
12(14)(9) = 63
Problem 3
A line perpendicular to y = 4x + 1 has what slope?
Worked answer
-1/4
Reciprocal of 4 is 14
Negated: -14
Problem 4
A line perpendicular to y = -25x + 3 has what slope?
Worked answer
5/2
Reciprocal: -52
Negated: 52
Problem 5
Find the line perpendicular to y = 34x - 5 through (8, 2).
Worked answer
y = -4x/3 + 38/3
m = -43
y - 2 = -43(x - 8)
y = -43x + 323 + 2 = -43x + 383
Problem 6
Are y = 3x + 1 and 2x + 6y = 5 perpendicular? Answer yes or no.
Worked answer
yes
Second: 6y = -2x + 5, so y = -13x + 56
3 × (-13) = -1
So yes
Problem 7
Perpendicular diagonals that bisect each other mean the shape is a
- rhombus
- rectangle
- trapezoid
- square
Worked answer
rhombus
Bisecting makes it a parallelogram.
Perpendicular makes it a rhombus.
Problem 8
A quadrilateral has diagonals that bisect each other, are congruent, and are perpendicular. Name it.
Worked answer
square
Bisecting: parallelogram.
Congruent: rectangle. Perpendicular: rhombus.
Both together: a square.