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: