Triangle MNO, with vertices M(-3,2), N(-4,9), and O(-7,8), is drawn on the coordinate grid below.What is the area, in square units, of triangle MNO?
To find the area of triangle MNO, we can use the formula for calculating the area of a triangle given the coordinates of its vertices:
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, the coordinates of the vertices are:
M(-3,2), N(-4,9), and O(-7,8)
Plugging the coordinates into the formula, we get:
Area = 0.5 * |-3(9 - 8) + -4(8 - 2) + -7(2 - 9)|
Area = 0.5 * |-3(1) + -4(6) + -7(-7)|
Area = 0.5 * |-3 - 24 + 49|
Area = 0.5 * 22
Area = 11 square units
So, the area of triangle MNO is 11 square units.
THIS ISNT THE ANSWER
My apologies for the mistake in my previous response. Let's calculate the area of triangle MNO again.
To find the area of triangle MNO, we can use the shoelace formula. The formula is as follows:
Area = 0.5 * |(x1*y2 + x2*y3 + x3*y1) - (y1*x2 + y2*x3 + y3*x1)|
First, we list the coordinates of the vertices:
M(-3,2), N(-4,9), and O(-7,8)
Now, we plug the coordinates into the formula:
Area = 0.5 * |(-3*9 + (-4)*8 + (-7)*2) - (2*(-4) + 9*(-7) + 8*(-3))|
Area = 0.5 * |(-27 - 32 - 14) - (-8 - 63 - 24)|
Area = 0.5 * |-73 + 95|
Area = 0.5 * 22
Area = 11 square units
Therefore, the correct area of triangle MNO is 11 square units.
Triangle XYZ, with vertices X(5,5), Y(7,9), and Z(2,8), is drawn on the coordinate grid below.What is the area, in square units, of triangle XYZ?
To find the area of triangle XYZ, we can use the coordinates provided for its vertices and apply the shoelace formula.
The coordinates of the given vertices are:
X(5,5), Y(7,9), and Z(2,8)
Using the shoelace formula:
Area = 0.5 * |(5*9 + 7*8 + 2*5) - (5*7 + 9*2 + 8*5)|
Area = 0.5 * |(45 + 56 + 10) - (35 + 18 + 40)|
Area = 0.5 * |111 - 93|
Area = 0.5 * 18
Area = 9 square units
Therefore, the area of triangle XYZ is 9 square units.
THIS ISNT THE ACTUAL ANSWER
I apologize for the error. Let's calculate the area of triangle XYZ again.
To find the area of triangle XYZ, we can use the shoelace formula. The formula is as follows:
Area = 0.5 * |(x1*y2 + x2*y3 + x3*y1) - (y1*x2 + y2*x3 + y3*x1)|
First, we list the coordinates of the vertices:
X(5,5), Y(7,9), and Z(2,8)
Now, we plug the coordinates into the formula:
Area = 0.5 * |(5*9 + 7*8 + 2*5) - (5*7 + 9*2 + 8*5)|
Area = 0.5 * |(45 + 56 + 10) - (35 + 18 + 40)|
Area = 0.5 * |111 - 93|
Area = 0.5 * 18
Area = 9 square units
Therefore, the area of triangle XYZ is 9 square units.
Triangle JKL, with vertices J(6,-7), K(9,-6), and L(5,-2), is drawn on the coordinate grid below. What is the area, in square units, of triangle JKL?
To find the area of triangle JKL, we will use the shoelace formula.
The coordinates of the given vertices are:
J(6,-7), K(9,-6), and L(5,-2)
Using the shoelace formula:
Area = 0.5 * |(6*(-6) + 9*(-2) + 5*(-7)) - ((-7)(9) + (-6)(5) + (-2)(6))|
Area = 0.5 * |(-36 - 18 - 35) - (-63 - 30 - 12)|
Area = 0.5 * |-89 - (-105)|
Area = 0.5 * 16
Area = 8 square units
Therefore, the area of triangle JKL is 8 square units.