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    If the area of the triangle whose vertices are (3,-2),(2,-3) and (p,-4) is 8 square units, then find the value of p.
    Question

    If the area of the triangle whose vertices are (3,-2),(2,-3) and (p,-4) is 8 square units, then find the value of p.

    A.

    -15

    B.

    17

    C.

    -16

    D.

    15

    Correct option is B

    Given:

    Vertices: (3, -2),(2, -3), and (p,−4)

    Formula used:

    The formula for the area of a triangle with vertices ​(x1,y1),(x2,y2),(x_1,y_1), (x_2,y_2), and (x3,y3)(x_3,y_3)

    Area=12x1(y2y3)+x2(y3y1)+x3(y1y2){Area} = \frac{1}{2} x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) ​​

    Solution:

    Given Vertices (3, -2),(2, -3), and (p,−4) 

    Substitute the values into the formula-

    8=12(3(3+4)+2(4+2)+p(2+3))8=\frac{1}{2}(3(−3+4)+2(−4+2)+p(−2+3))

    8=12(3(1)+2(2)+(1))8=\frac{1}{2}(3(1)+2(−2)+(1))

    8 = 12\frac{1}{2} [3 - 4+ p]

    8= 12\frac{1}{2} (p-1)

    16 = p-1

    p-1 = 16

    values of p -

    p - 1 = 16

    p = 17
    The values of p are 17

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