Find the orthocenter& circumcenter of a triangle when their vertices are A(1, 2), B(2, 6), C(3,-4). => Please don't spam or answer Irrelevantly.​

iven, the vertices of the triangle,  

A=(1,2)

B=(2,6)

C=(3,−4)

Slope of AB

=x2​−x1​y2​−y1​​=2–16−2​=14​=4

Slope of CF

= Perpendicular slope of AB

=  

Slope of AB

−1  =−14

The equation of CF is given as,

y–y  

1

​  

=m(x–x  

1

​  

)

y+4=−14(x–3)

4y+16=−x+3

x+4y=−13 ——————————– (1)

Slope of BC

=  

x  

2

​  

–x  

1

​  

y  

2

​  

–y  

1

​  

​  

=  

3–2

−4–6

​  

=  

1

−10

​  

=−10

Slope of AD

=Perpendicular slope of BC

=  

Slope of BC

−1

​  

=  

−10

−1

​  

=  

10

1

​  

The equation of AD is given as,

y–y  

1

​  

=m(x–x  

1

​  

)

y+2=  

10

1

​  

(x–1)

10y+20=x–1

x–10y=21 ——————————– (2)

Subtracting equation (1) and (2),

x+4y=−13

−x+10y=−21

——————

14y=−34

y=−2.429

Substituting the value of y in equation (1),

x+4y=−13

x+4(−2.429)=−13

x–9.714=−13

x=−3.286

Orthocenter =(−3.286,−2.429)

Step-by-step explanation:

you can't solve x because it is 2 linear equation and you only have one equation