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grade 10 math- slope/midpoint/length formulas

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

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


  • two-point form/Distance formulas - ,

    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)

    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.

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

  • grade 10 math- slope/midpoint/length formulas - ,


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