(a) Two lines meet at a point that is also the endpoint of two rays.

​Part A
​
​Which equation can be used to determine the value of ?
​
A x+4x=90
B x+4x+27=180
C x+27+63=90
D x+4x+27+90=180
(b)
​
​Part B
​
​What is the value of x?

​ x=________________

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).