Find the point on the line y=2x that is closest to the point (4, 5) .
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Answer:
The coordinates of C is (-8,1)
Step-by-step explanation:
Looking at the attached image, you'd see that, AB is 1 and BC is 1, that's because we are told that ratio of AB to AC is 1:2 meaning, AC is 2 and AB is 1. Therefore for that ratio to be satisfied BC has to be 1 so that AC would be 2.
Now let's assume the coordinates of C is .
To get it's coordinates, we use the section formula:
Where (m,n) is the (AB, BC)
Therefore we have
This gives:
and
From there x = -8 and y = 1
Therefore the coordinates of C is (-8, 1).
