Geometry unit 7 lesson 7. picture attached.

The coordinates of orthocenter of the triangle are (1,5).

Step-by-step explanation:

The given vertices are A(0,6), B(4,6) and C(1,3).

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

The product of slopes of two perpendicular lines is -1.

The slope of AB is

The slope of AB is 0, therefore slope of line which is perpendicular to AB is .

Point slope form of a line is

Where, m is the slope.

The equation of altitude on AB form C is

                             ..... (1)

Slope of BC is

The slope of BC is 1 therefore the slope of altitude on BC from A is -1.

The equation of altitude on BC from A is

                        ..... (2)

Using (1) and (2) we get

The  intersection point of two altitudes is (1,5). Therefore coordinates of orthocenter of the triangle are (1,5).

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: