Analytic Geometry Challenge

Listen up Cyber-Students:

If you can solve this question efficiently and accurately, you know your stuff.

Reproduce the diagram on graph paper, then solve the question
making sure to show your work.

If you run into problems, bring your work to our next session so we can fix them.

Go to it.

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We need to build InterPlum St. in 2 sections

the first // to the other Plum Sts. such that HM = 1.5(ML).

This section runs until it meets Blue St. at J, then changes course to meet ThinRed St. at R

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Solutions

Since angle LGO = 45º, the slope of LR must be -1,
since the rise over run for this line is in ratio 1 : 1. (isosceles right triangle).

This means that G is at (20, 0). (45 - 25 since OT = 45 and GT = 25).
So, L is at (0, 20).

a) The equation of LoPlum St (LR) is y = - x + 20.

b) The equation of HiPlum St (HS) is y = - x + 50.

c) L is at (0, 20), H is at (0, 50), S is at (45, 5)

d) M is at (0, 32) (HM : ML = 3 : 2, 5 parts = 30, 1 part = 6)

e) i) The equation of InterPlum St (MJ) is y = - x + 32

ii) J is at (32, 0) and R is (45, - 25) so the slope of JR is -25 / 13.
The equation of JR is

f)

The total length of InterPlum St. is 73.43 Km.

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