COORDINATE
GEOMETRY
TERM 2
YEAR 10
2022-2023
10th
Grade
Syllabus
C3.1
Demonstrate familiarity with Cartesian coordinates in two dimensions.
C.3.2
Find the gradient of a straight line.
C3.3
Calculate the length and the coordinates of the midpoint of a straight line
from the coordinates of its end points.
E3.4
Interpret and obtain the equation of a straight-line graph in the form 𝑦 =
𝑚𝑥 + 𝑐.
E3.5
Determine the equation of a straight line parallel to a given line.
E3.6
Find the gradient of parallel and perpendicular lines.
TABLE OF CONTENTS
01
GRADIENT
03
EQUATION OF STRAIGHT
LINE
You can describe the
topic of the section here
You can describe the
topic of the section here
02
LINE SEGMENT
You can describe the
topic of the section here
01
Gradient of a
Straight Line
Gradient is the slope of a line.
INTRODUCTION
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
We observe that,
If 𝐴(𝑥1 , 𝑦1 ) and 𝐵(𝑥2 , 𝑦2 ) are two points on a
line, then
A PICTURE IS WORTH A THOUSAND WORDS
LET'S PRACTICE
Mercury is the closest planet to
the Sun and the smallest one in
the Solar System—it’s only a bit
larger than the Moon
LET'S PRACTICE
LET'S PRACTICE
LET'S PRACTICE
02
LENGTH OF A
LINE SEGMENT
A line segment is part of a line
with two end-points.
General Form
Consider any two points P and Q with
coordinates 𝑥1 , 𝑦1 and 𝑥2 , 𝑦2 respectively.
By completing the right-angled ∆𝑃𝑄𝑅 , we
have the coordinates of R as 𝑥2 , 𝑦1 .
Hence 𝑃𝑅 =
And 𝑄𝑅 =
𝑃𝑄2 = 𝑃𝑅2 + 𝑄𝑅2
𝑃𝑄2 =
In general, the length of any line segment
PQ, where the coordinate of the points P
𝑥1 , 𝑦1 and Q 𝑥2 , 𝑦2 is
𝑃𝑄 = 𝑥2 − 𝑥1 2 + 𝑦2 − 𝑦1 2
Using the Length to show that a Triangle is
Right-angled
The Midpoint
of a Line
Segment
(っ◔◡◔)っ ♥ MIDPOINTS ♥
03
EQUATION OF STRAIGHT LINE
𝑦 = 𝑚𝑥 + 𝑐
WHAT DOES IT STAND FOR?
𝑦 = 𝑚𝑥 + 𝑐
c
PRACTICE
“This is a quote, words full of wisdom
that someone important said and can
make the reader get inspired.”
—SOMEONE FAMOUS
PARALLEL LINES
How do we know when two lines are parallel?
Answer:
The gradient of y=2x+1 is: 2
The parallel line needs to have the same
slope of 2.
y − y1 = 2(x − x1)
And then put in the point (5,4):
y − 4 = 2(x − 5)
y − 4 = 2x − 10
y = 2x − 6
PERPENDICULAR LINES
Two lines are Perpendicular when they meet at a
right angle (90°).
The gradient of y=-4x+10 is: -4
The negative reciprocal of that slope is:
−1 1
𝑚=
=
−4 4
So, the perpendicular line will have a slope of
1/4.:
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
And now put in the point (7,2):
1
𝑦−2 = 𝑥−7
4
1
1
𝑦= 𝑥+
4
4
Write the equation in slope-intercept form of the line
that is parallel to the graph of each equation and
passes through the given point.
a.
y = 3x + 6; (4, 7)
b.
y = x – 4; (-2, 3)
c.
y = ½ x + 5; (4, -5)
d.
y + 2x = 4; (-1, 2)
Write the equation in slope-intercept form of the line
that is perpendicular to the graph of each equation and
passes through the given point.
a.
y = -5x + 1; (2, -1)
b.
y = 2x – 3; (-5, 3)
c.
y = -4 x - 2; (4, -4)
d.
7y + 4x = 3; (-4, -7)