## Orthocenter of a Triangle ABC

How to Find the orthocenter of a Triangle

The orthocenter of a triangle is where all of the altitudes of a triangle meet each other.

The altitude is a perpendicular line segment from a vertex of a triangle to the opposite side (Vertex A to side BC).

To draw the orthocenter, first You draw the triangle on a coordinate plane and draw all three altitudes (one from each vertex of the triangle) and determine the point at which they all intersect. This intersection is a orthocenter of a Triangle ABC.

## Substitution Method

Calculate value of x and y: Equations are y-x = 3 and 2(x + y) = 14

Solution:
In substitution method, we have a given equation of two variables, x and y.
First, divide in second equation by 2 in both sides.
x + y = 4 …. (1)
y – x = 3 => y = x + 3 ….(2)
Now, put the value of y in equation 1 and solve the equation for x, i.e
x + (x + 3) = 4
x + x + 3 = 4
2x = 4 –3
which gives x = 1/2.

Now, substitute x = 1/2 in any one of the given equation and find the value of y
y = 1/2 + 3
y = 7/2
Answer is : x = 1/2, y = 7/2

## Solving Linear Equation of One Variable - Math Watch Video

Solve for X:
2/3 X + 1 = X/6 x 3

In given equation, we find the value of X.

We see that, the denominator of the given equation is 6, so we just multiplied the whole equation by 6.
6 (2/3 X + 1) = 6(X/6 x 3)

Using the distributive law, we have
4X + 6 = 3X

Now taken out the common terms in single side
4X –3X = –6

which gives
X = –6
Answer is : x = –6

## Solving Linear Equation by Substitution Method Algebra Watch Video

Q.
4x + 3y = 1 and x = 1 – y
Solution:
In substitution method, we have a given equation of two variables, x and y.
First you put the value of x in other given equation 4x = 2x + 3y and calculate the value of y.
Steps are:
x = 1 –y
Plug ‘x’ in first equation.
4(1 –y) + 3y = 1
Solve this equation for y
4 –4y + 3y = 1
4 –y = 1
y = 3
Substitute y = 1 in any one of the given equation and find the value of other variable
x = 1 –y
x = 1 –3 = –2
Answer is : x = –2, y = 3

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