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WORKBOOK
THE COORDINATES OF CENTROID (CENTER OF GRAVITY) OF A TRIANGLE
Given the coordinates of the three vertices of a triangle
ABC, A(x 1, y 1), B(x 2, y 2), C(x 3, y 3)
The centroid G(x, y) is given by the following formula;
x x x y y y
x 1 2 3 and y 1 2 3
3 3
Ex: Given the coordinates of the three vertices of a triangle ABC, A(–6, 7), B(–3, 6) and C(3, 2) find
the distance between its center of gravity and origin.
SLOPE OF A LINE
The Slope (gradient) of a line d is defined to be the ratio of
change in y to change in x and denoted by m d .
If Δ Δ are representing change in y and change in x ,
then the slope (gradient) of line d is
y
m as shown in the figure
d
x
rise
If we call Δ as rise and Δ as run, then m
d
run
Since the ratio y is the tangent of the angle that the line d makes with the x axis, we can
x
define the slope of the line d as the tangent of the angle θ,
=
Note that, slopes of the lines inclined to right is positive while the slopes of the lines
inclined to left is negative.
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102math-wb-w3-(Vector)
