geometry

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On a graph, the points (4,-2),(7,-2),(9,-5) and (2,-5) are connected in order to form a trapezoid. To the nearest tenth, what is its perimeter?

  • geometry -

    Compute the four side lenghts using the pairs of coordinates.

    The side that goes from (4,-2) to (7,-2) has a length of sqrt[(7-4)^2 + (2 -(-2)^2] = 5

    Do the others the same way.

    Then add all four.

  • geometry -

    Thank you for your help, I still don't understand

  • geometry -

    In order to figure the length of a line segment, you have to rely on the Pythagorean Theorem. If that doesn't sound familiar, you need to review your text. The theorem states that in a right triangle with legs a and b, with hypotenuse c,

    c2 = a2 + b2

    Now, if you plot two points on a piece of graph paper, such as (7,-2) and (9,-5), the line joining the points will be a slanting line. If you draw horizontal and vertical lines from each point, they will intersect to form a right triangle. The length of the legs are just the x-distance from 7 to 9 = 2, and the y-distance from -5 to -2 = 3.

    So, the length of the hypotenuse is given by

    h2 = 22 + 32
    h2 = 13
    so,
    h = √13

    If you follow these steps for each side of the figure, you can add up all the lengths to get the perimeter.

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