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Math Help - need help on problem 2

  1. #1
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    need help on problem 2

    hi, i thought id start a new thread for the 2nd problem since the 1st problem went for 2 pages

    Problem 2

    Find the distance (correct to three decimal places) from the point (-5,-2) to the line 3x+y=8. Hint: the distance from a point to a line is the perpendicular distance.

    please help!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by zazeem View Post
    hi, i thought id start a new thread for the 2nd problem since the 1st problem went for 2 pages

    Problem 2

    Find the distance (correct to three decimal places) from the point (-5,-2) to the line 3x+y=8. Hint: the distance from a point to a line is the perpendicular distance.

    please help!!
    first thing's first, find the line that's perpendicular to y = -3x + 8 that passes through (-5,-2). since the line is perpendicular, its slope is the negative inverse of the original line, namely, 1/3. now we use the point-slope form to find our line:

    y - y_1 = m(x - x_1)

    \Rightarrow y + 2 = \frac 13(x + 5)

    \Rightarrow y = \frac 13x - \frac 13

    now we need to know where these lines meet. so we set them equal to each other:

    -3x + 8 = \frac 13x - \frac 13

    \Rightarrow \boxed{x = \frac 52}

    plug this x-value into either line and you will find the corresponding y-value to be \boxed{y = \frac 12}

    thus you want to use the distance formula to find the distance between the points (-5,-2) and (5/2, 1/2)

    can you continue? perhaps more importantly, do you understand what i did?
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