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Triangle SKY with vertices S(-6,-5),K(-1,-2),and Y(-4,-7),(0,7)

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Answer:

To find the area of triangle SKY with vertices S(-6,-5), K(-1,-2), and Y(-4,-7), we can use the Shoelace Formula. Here are the steps:

1. Write down the coordinates of the vertices of the triangle: S(-6,-5), K(-1,-2), and Y(-4,-7).

2. Label the x-coordinates as x1, x2, and x3, and the y-coordinates as y1, y2, and y3.

- x1 = -6, y1 = -5

- x2 = -1, y2 = -2

- x3 = -4, y3 = -7

3. Write out the Shoelace Formula:

Area = 1/2 * |(x1*y2 + x2*y3 + x3*y1) - (y1*x2 + y2*x3 + y3*x1)|

4. Substitute the values into the formula:

Area = 1/2 * |((-6*-2) + (-1*-7) + (-4*-5)) - ((-5*-1) + (-2*-4) + (-7*-6))|

= 1/2 * |(12 + 7 + 20) - (5 + 8 + 42)|

= 1/2 * |39 - 55|

= 1/2 * |-16|

= 8

5. The absolute value of -16 is 16, so the area of triangle SKY is 8 square units.

Therefore, the area of triangle SKY with vertices S(-6,-5), K(-1,-2), and Y(-4,-7) is 8 square units.

Explanation:

User Andrew Killen
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