Answer:
Step-by-step explanation: To find the area of the polygon with the given vertices J(-3,4), K(4,4), and L(3,-3), you can use the formula for the area of a triangle formed by these points. The formula for the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, you have three vertices: J(-3,4), K(4,4), and L(3,-3). Plug these coordinates into the formula:
Area = 1/2 * |-3(4 - (-3)) + 4((-3) - 4) + 3(4 - 4)|
Now, calculate the values inside the absolute value bars:
Area = 1/2 * |-3(7) + 4(-7) + 3(0)|
Area = 1/2 * |-21 - 28 + 0|
Now, simplify the expression inside the absolute value bars:
Area = 1/2 * |-49|
Since the absolute value of -49 is 49:
Area = 1/2 * 49
Now, multiply 1/2 by 49:
Area = (1/2) * 49 = 49/2
So, the area of the polygon with vertices J(-3,4), K(4,4), and L(3,-3) is 49/2 square units, which can be expressed as 24.5 square units.