About Orthocenter Formula
The Greek word "ortho" means "right." The centre of all right angles is represented by the orthocenter formula. It is drawn from vertices to the heights on the opposite sides. This concept is crucial for comprehending a triangle's varied features in relation to its other dimensions. The height of a triangle is the line that passes through the vertex and is perpendicular to the opposing side. As a result, elevations are created by each vertex of a triangle.
The orthocenter is the point where the heights of a triangle intersect. The orthocenter formula can be used to find the coordinates of a triangle's orthocenter. Let's take a closer look at the orthocenter formula.
Let us consider a triangle PQR
PA, QB, RC are perpendicular lines drawn from three vertices P(x1,y1), Q(x2,y2), and R(x3,y3)respectively of the ?PQR. H(x,y) is the intersection point of the three altitudes of the triangle.
Step1. Using the formula: m, get the slope of the triangle's sides (slope)
- = y2 − y1/x2 − x1
- Let mPR be the slope of the PR.
- Thus,
- mPR = y3 − y1/x3 − x1
- Similarly,
- mQR = y3 − y2/x3 − x2
Step2. The slope of the ?PQR's altitudes will be perpendicular to the slope of the triangle's sides.
We know,
- Perpendicular slope of line = −1/slope of the line=−1/m
- The slope of the respective altitudes:
- Slope of PA,
- mPA = −1/mQR
- Slope of QB,
- mQB =−1/mPR
To compute the equations of the lines intersecting PA and QB, we'll utilise the slope-point form equation as a straight line.
Using arbitrary points, a generalised equation is therefore generated x and y is:
mPA=(y − y1)/(x − x1)
mQB=(y − y2)/(x − x2)
The orthocenter of a triangle can be computed by solving the two equations for any given values???????
Get a List of Maths Formulas on one page
Download the pdf of Orthocenter Formula
