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Taylor129
29.06.2019 •
Mathematics
in the diagram, c and d are located such that ab is divided into three equal parts. what are the coordinates of c and d?
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Ответ:
Step-by-step
Topic: Points of division
There are scary looking formulas that can be used, but it is much easier to calculate by reasoning.
Given : A(-3,6), B(6,-3)
Solution:
The idea is to subdivide the DIFFERENCE in coordinates into thirds, and add onto that of A. We choose A as the starting point, but method works equally well if we chose B.
Difference in coordinates (delta) between A & B is then
delta(Bx-Ax, By-Ay)
=(6-(-3), -3-6)
=delta(9, -9)
One third of difference (for point C)
=delta/3 = (3,-3)
So coordinates of point C
= A(-3,6)+(3,-3)
= C(0,3)
Two thirds of difference (for point D)
= (2/3)delta = (6, -6)
Coordinates for point D
= A(-3,6)+(6,-6)
= D(3,0)
If you prefer to use formulas, it would be
New coordinates = (Xa+(Xb-Xa)*k, Ya+(Yb-Ya)*k)
where
Xa,Xb = x-coordinates of points A & B respectively.
Ya,Yb = y-coordinates of points A & B respectively.
k=ratio (usually less than 1)
Here
k for point C = 1/3
k for point D = 2/3
Ответ:
B.
Step-by-step explanation: