Triangle XYZ, with vertices X(3,-7), Y(7,-4), and Z(4,-3), is drawn inside a rectangle, as shown below.What is the area, in square units, of triangle XYZ?
To find the area of triangle XYZ, we can use the formula for the area of a triangle given its vertices:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, we have:
x1 = 3, y1 = -7
x2 = 7, y2 = -4
x3 = 4, y3 = -3
Plugging these values into the formula, we get:
Area = 1/2 * |3(-4 - (-3)) + 7(-3 - (-7)) + 4(-7 - (-4))|
Area = 1/2 * |3(-1) + 7(4) + 4(-3)|
Area = 1/2 * |-3 + 28 - 12|
Area = 1/2 * 13
Area = 6.5 square units
Therefore, the area of triangle XYZ is 6.5 square units.
THIS ISNT THE RIGHT ANSWER
I apologize for the error. Let us try to find the correct answer by using the vertices of the triangle to calculate the area.
We can calculate the area of a triangle given the coordinates of its vertices using the formula:
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, the coordinates of the vertices are X(3, -7), Y(7, -4), and Z(4, -3).
Substitute these values into the formula:
Area = 0.5 * |3(-4 - (-3)) + 7(-3 - (-7)) + 4(-7 - (-4))|
Area = 0.5 * |3(-4 + 3) + 7(-3 + 7) + 4(-7 + 4)|
Area = 0.5 * |3 * -1 + 7 * 4 + 4 * -3|
Area = 0.5 * |-3 + 28 - 12|
Area = 0.5 * 13
Area = 6.5 square units
Therefore, the correct area of triangle XYZ is 6.5 square units.
Triangle ABC, with vertices A(-9,4), B(-5,3), and C(-4,9), is drawn inside a rectangle, as shown below. What is the area, in square units, of triangle ABC?
To find the area of triangle ABC, we can use the formula for the area of a triangle given its vertices:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, we have:
x1 = -9, y1 = 4
x2 = -5, y2 = 3
x3 = -4, y3 = 9
Plugging these values into the formula, we get:
Area = 1/2 * |-9(3 - 9) + (-5)(9 - 4) + (-4)(4 - 3)|
Area = 1/2 * |-9(-6) + (-5)(5) + (-4)|
Area = 1/2 * (54 - 25 - 4)
Area = 1/2 * 25
Area = 12.5 square units
Therefore, the area of triangle ABC is 12.5 square units.