Linear graphs: find a line 2 - perpendicular

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Ruth Hand

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2 years, 7 months ago

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Christian Lawson-Perfect 2 years, 5 months ago

Published this.

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Ruth Hand 2 years, 7 months ago

Gave some feedback: Ready to use

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Ruth Hand 2 years, 7 months ago

Created this as a copy of Linear graphs: find a line 1 - parallel.

Name	Status	Author	Last Modified
Linear graphs: find a line 1 - parallel	Ready to use	Ruth Hand	16/01/2023 14:16
Linear graphs: find a line 2 - perpendicular	Ready to use	Ruth Hand	16/01/2023 14:15
Linear graphs: find a line 3 - parallel or perpendicular	Ready to use	Ruth Hand	16/01/2023 14:14

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Question statement

Find the equation of a line given a point and a perpendicular line.

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

pops	integer	0
x	integer	-2
y	integer	0
a	integer	2
b	integer	3
c	integer	-4
m	rational	-2/3
pop	string	perpendicular
l1	vector	vector(1,0.6666666667)
l2	vector	vector(2,0)
point	vector	vector(-2,0)
apps	ggbapplet	HTML node
newm	rational	3/2
newc	rational	3
apps2	ggbapplet	HTML node
popgrad	string	be the inverse reciprocal
vec	vector	vector(1,4.5)
d	rational	4/3

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Name

Data type

Value

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Description

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Generated value: `integer`

→ Used by:

newm
pop
popgrad

This variable doesn't seem to be used anywhere.

Advice

{apps}

Rearrange the given equation to find the gradient:

\[ \simplify[all]{{a}x + {b}y + {c} = 0} \]

\[ y = \simplify[FractionNumbers]{{-a/b}x-{c/b}} \]

Therefore the gradient, $m_1$, is equal to $\simplify[FractionNumbers]{{m}}$.

Since we want the {pop} line, then the gradient of the new line, $m_2$, will {popgrad}, and therefore $m_2 = \simplify[FractionNumbers]{{newm}}$.

{apps2}

We can now take the equation $y = mx + c$, and subsitute in $m_2$ along with $(x,y) = (\var{x},\var{y})$, to give:

\[ \var{y} = \simplify[FractionNumbers]{{newm}} \times \simplify[FractionNumbers]{{x}} + c \]

and rearrange to calculate

\[ c = \simplify[FractionNumbers]{{y} - {newm}*{x}} \]
\[ c = \simplify[FractionNumbers]{{y - newm*x}} \].

Therefore

\[y = \simplify[FractionNumbers]{{newm}*x +{y - newm*x}}\].

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This question is used in the following exams:

All the good stuff by Chris Templet in Chris's workspace.
Quiz 1 by Kate Vincent in Kate's workspace.
Subject Knowledge Homework 1 by Ciaran Cassidy in A Level Subject Knowledge Homework.
extension quiz by Billy Woods in Billy's workspace.
Knowledge graph test by Benita Nel in UWC test space.

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Linear graphs: find a line 2 - perpendicular

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Taxonomy: mathcentre

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Taxonomy: Context

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Christian Lawson-Perfect 2 years, 5 months ago

Ruth Hand 2 years, 7 months ago

Ruth Hand 2 years, 7 months ago

Error in variable testing condition

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Generated value: `integer`

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Linear graphs: find a line 2 - perpendicular

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 5 months ago

Ruth Hand 2 years, 7 months ago

Ruth Hand 2 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`