Question

On the coordinate plane, the segment from M(-1, -3) to NC-1, 5) forms one side of Triangle MNO.

The triangle has an area of 24 square units. Select all of the points where O could be.

(5,8)

(-7, -3)

(-4,5)

(4, -7)

Answer 1

To find the possible points where O could be in the triangle MNO, calculate the distance between point O and the line formed by the segment MN. If the distance is equal to the height of the triangle, then the point is a possibility. In this case, the points where O could be are (5, 8) and (-4, 5).

Step-by-step explanation:

To find the possible points where O could be, we need to determine the third coordinate of point O in the triangle MNO. We know that the area of the triangle is 24 square units. The formula to find the area of a triangle is Area = 1/2 * base * height.

We can find the base of the triangle by calculating the distance between points M and N, which is 8 units. To find the height, we use the formula for the distance between a point and a line, which is: Distance = |Ax + By + C| / sqrt(A^2 + B^2), where the line equation is in the form Ax + By + C = 0, and (x, y) is the point. The equation of the line passing through points M and N is x = -1.

Using the distance formula, we can calculate the distance between point O and the line. For example, for point (5, 8), the distance is: Distance = |-1 * 5 + 0 * 8 - 1| / sqrt((-1)^2 + 0^2) = 6 / sqrt(1) = 6 units.

If the distance between point O and the line is equal to the height of the triangle, then point O is a possible point. Therefore, the points where O could be are: (5, 8) and (-4, 5).