Using proportions, the points are given as follows:
12. X(1.25, 4).
13. Y(4.67, 0).
14. Z(3.2, 0).
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Item 12
The coordinates are:
A = (-1,4), B = (8,4).
AX to XB is 1:3, hence the proportional equation is:
X - A = 1/4(B - A)
The x-coordinate of X is found as follows:
x + 1 = 1/4(8 + 1)
x + 1 = 2.25
x = 1.25.
The y-coordinate of X is found as follows:
y - 4 = 1/4(4 - 4)
y = 4.
Hence the point is X(1.25, 4).
Item 13
The coordinates are:
C(2,2), D(10,-1).
DY to YC is 2:1, hence the proportional equation is:
Y - C = 1/3(D - C)
The x-coordinate of Y is found as follows:
x - 2 = 1/3(10 - 2)
x - 2 = 2.67.
x = 4.67
The y-coordinate of Y is found as follows:
y - 1 = 1/3(-1 - 2)
y - 1 = -1
y = 0.
Hence the point is Y(4.67, 0).
Item 14
The coordinates are:
E(2,-2), F(5,3)
EZ to ZF is 2:3, hence the proportional equation is:
Z - E = 2/5(F - E)
The x-coordinate of Z is found as follows:
x - 2 = 2/5(5 - 2)
x - 2 = 1.2
x = 3.2.
The y-coordinate of Z is found as follows:
y + 2 = 2/5(3 + 2)
y + 2 = 2
y = 0.
Hence the point is Z(3.2, 0).
More can be learned about proportions at https://brainly.com/question/24372153
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