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Math Help - Find the Value of k

  1. #1
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    Find the Value of k

    The vertices of Triangle PQR are P(1, 2), Q(-3, 6) and
    R(4, 8). A line through Q is parallel to line segment PR and passes through point (k, 14). Find k.

    MY WORK:

    I know that parallel lines have equal slopes. I first found the slope of line segment PR to be 2/1.

    I then equated the slope this way:

    2/1 = (14 - 2)/(k - 1)

    Solving for k, I got k = 7 but the answer is k = 1.

    What did I do wrong and why is the answer 1 not 7?

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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    The vertices of Triangle PQR are P(1, 2), Q(-3, 6) and
    R(4, 8). A line through Q is parallel to line segment PR and passes through point (k, 14). Find k.

    MY WORK:

    I know that parallel lines have equal slopes. I first found the slope of line segment PR to be 2/1.

    I then equated the slope this way:

    2/1 = (14 - 2)/(k - 1)

    Solving for k, I got k = 7 but the answer is k = 1.

    What did I do wrong and why is the answer 1 not 7?
    Hello Magentarita,

    You used the wrong two points. You used point P instead of point Q.

    Q(-3, 6) and X(k, 14)

    Line QX will have a slope of 2 as you indicated.

    \frac{14-6}{k-^-3}=\frac{2}{1}

    This will get you to your desired result.
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  3. #3
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    ok...........

    Quote Originally Posted by masters View Post
    Hello Magentarita,

    You used the wrong two points. You used point P instead of point Q.

    Q(-3, 6) and X(k, 14)

    Line QX will have a slope of 2 as you indicated.

    \frac{14-6}{k-^-3}=\frac{2}{1}

    This will get you to your desired result.
    I used the wrong points. No wonder I ended up with the wrong answer for k. I really enjoy geometry.
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