For triangle mnp with vertices m (-4, -2), n (6, -2), and p -2, 10). find the coordinates of each one. the centroid the orthocenter

The centroid of MNP is and the orthocenter of the MNP is .

Step-by-step explanation:

The vertices of triangle are M (-4, -2), N (6, -2), and P (-2, 10).

Centroid of a triangle is the intersection point of all medians.

Formula for centroid

The centroid of MNP is

Orthocenter of a triangle is the intersection point of all altitudes.

We have to find the intersection of at least two altitudes.

Slope of a line is

From the figure it is noticed that the line MN is a horizontal line, slope of MN is

The product of slopes of perpendicular lines is -1. Therefore the product of slopes of MN and AP is -1.

Point slope form

Where m is slope.

Equation of AP is

                          ..... (1).

Slope of MP is

The product of slopes of perpendicular lines is -1. Therefore the product of slopes of MP and NB is -1.

Equation of NB is

           ..... (2)

Using equation (1) we get

Therefore the orthocenter of the triangle is .

step-by-step explanation:

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