Question

Triangle MNO has the vertices shown. M(-8, 1) N (-4,4) O (-2,1) What is the area of triangle MNO, in square units?​

Answer 1

The area of triangle MNO with vertices at M(-8, 1), N (-4,4), and O (-2,1) is calculated using the coordinate geometry method and is found to be 9 square units.

Step-by-step explanation:

To calculate the area of triangle MNO with vertices M(-8, 1), N (-4,4), and O (-2,1), we can use the coordinate geometry method. The formula for the area of a triangle with vertices at (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by:

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

Substituting our points into this formula:

Area = |(1/2) × [(-8(4-1) + (-4)(1-1) + (-2)(1-4))]|
Area = |(1/2) × [(-8 × 3) + (-4 × 0) + (-2 × -3)]|
Area = |(1/2) × [-24 + 0 + 6]|
Area = |(1/2) × (-18)|
Area = |-9|

The area is always a positive value, so the area of triangle MNO is 9 square units.

Answer 2

The area of triangle MNO is calculated by using the coordinates of its vertices to find the base and height, then applying the formula for the area of a triangle. The resulting area of triangle MNO is 6 square units.

Step-by-step explanation:

To find the area of triangle MNO, we can use the formula for the area of a triangle, which is 1/2 × base × height. However, first, we need to determine the base and height of triangle MNO. By looking at the coordinates of the vertices, we can choose line segment MN as the base because it is parallel to the x-axis, which makes calculating the height straightforward.

The coordinates for M and N are M(-8, 1) and N(-4, 4), respectively. The base MN is the difference in the x-coordinates of N and M, which is |(-4) - (-8)| = |4 - 8| = 4 units. The height can be determined by the difference in y-coordinates of vertex O and the base line MN. Since point O has a y-coordinate of '1' (the same as point M), and point N has a y-coordinate of '4', the height is |4 - 1| = 3 units.

Now that we have the base and height values, we can calculate the area:

Area = 1/2 × base × height
Area = 1/2 × 4 units × 3 units
Area = 1/2 × 12
Area = 6 square units.

Therefore, the area of triangle MNO is 6 square units.