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How to find the orthocenter of a triangle when finding the trouble: the lines x=2, y=3 and 3x+2y=6 at the point. Can someone give me some good tips?

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We know that the orthocentre of a right triangle is at the vertex forming right angle. Here, x=2 and y=3 are perpendicular sides of the given triangle. So, their point of intersection i.e., (2,3) is the orthocentre.

@lawsonwolf gave the sample for you to understand it and hope it was helpful

In this sample, The orthocenter of the triangle A1A2A3 is point H. The altitudes A1H1, A2H3, and A3H3 meet at the point H. Thus, @lawsonwolf says it ok “The Orthocenter of a Triangle is the point at which the three altitudes of the triangle are meet each other”

I will give you one real sample here

The orthocentre of a right triangle is at the vertex forming right angle.

x=2 & y=3 are perpendicular sides of the given triangle.

Thus, the orthocentre is their point of intersection i.e., (2,3)

The Orthocenter of a Triangle is the point at which the three altitudes of the triangle are meet each other

With x=2 is the parallel line to y, and constant value of x=2 (perpendicularly to x), similarly y=3 which is perpendicular line to y, and with constant y coordinate = 3, and parallel to to x

You can see that you are basically getting a right angle triangle. The vertex of the triangle at right angle is located at 2,3. Whose orthocentre? It is possible to get it by tracing three lines.