VC2M9A04 Official strand: Algebra

Gradient, midpoint and distance

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Use coordinate differences and averages to measure a segment in the Cartesian plane.

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Find the gradient of the segment from A(-5, -1) to B(-3, -3).

A1 B-1 C0 D2

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Answer: -1

The vertical change is -3 − (-1) = -2.
The horizontal change is -3 − (-5) = 2.
Gradient = rise/run = -1.
(-2) ÷ 2 = -1.

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Curriculum reference

Victorian Curriculum F–10 Version 2.0

Pi Leo practice scope

Use coordinate differences and averages to measure a segment in the Cartesian plane.

Read the official VCAA curriculum description (VC2M9A04)

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VC2M9A04-C01Calculate rise divided by run.
VC2M9A04-C02Use coordinate averages for midpoint and Pythagoras for distance.
VC2M9A04-C03Create a coordinate construction and verify it digitally.
VC2M9A04-C04Apply and explain gradient, midpoint and distance using read and connect representations.
VC2M9A04-C05Apply and explain gradient, midpoint and distance using work backwards from what is known.

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Subskills

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Descriptor-derived subskills

D01
Measure the slopeCalculate rise divided by run.
D02
Locate the middle and measure lengthUse coordinate averages for midpoint and Pythagoras for distance.
D03
Read and connect representationsApply and explain gradient, midpoint and distance using read and connect representations.
D04
Work backwards from what is knownApply and explain gradient, midpoint and distance using work backwards from what is known.