A map shows a main gas pipeline running straight from A(45,60) to B(65,40)

Question

a) Is the point C(63,54) on the branch pipeline? Explain your reasoning

b) What is the shortest route for connecting point C to the main pipeline.Explain

**OMGGGG PLZZZ HELPPP, THANK YOUUUUUU!!!!!!!!!!!

Answer 1

The equation of a line passing two given points P1(x1,y1) and P2(x2,y2) is:
(y-y1)/(y2-y1) = (x-x1)/(x2-x1)
Substitute the coordinates of the two given points and simplify to find the formula of the line, L1.
(hint: The equation I get is Ax+By+C=0 where C is -105)

a.
Substitute the value of x of the third point (P3) into L1 and see if the corresponding value of y equals the y-coordinate of P3.

b.
The distance of the point P3(x3,y3) from a line Ax+By+C=0 is given by
|Ax+By+C|/sqrt(A²+B²)
I get about 8.5.

Answer 2

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