Hello! The answer to your question is B, the intersection of the lines drawn to bisect each vertex of the triangle. Hope this helped! Please pick my answer as the Brainliest!
The orthocenter of the triangle will be the intersection of the three altitudes of a triangle. The orthocenter has several vital properties with other parts of a triangle, including the area ,incenter circumcenter and more. Typically, the orthocenter is represented by letter H.
The altitude of a triangle is a line that passes through the vertex of a triangle and it is also perpendicular to the opposite side. The orthocenter of a triangle can lie outside the triangle because an altitude may not necessarily intersect the side.
C. Obtuse Triangle
The orthocenter of a triangle is inside when the triangle is acute, on the triangle when it's a right triangle, and outside when it's obtuse
C. obtuse triangle
It turns out that all three altitudes always intersect at the same point - the so-called orthocenter of the triangle. The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside. To make this happen the altitude lines have to be extended so they cross.
See the attached
When in doubt, draw a diagram.
The orthocenter of this acute triangle will be within its bounds. That should tell you right away that the y-coordinate of it will not be 8, but must be between 2 and 6.
The line perpendicular to BC through A must have a y-intercept greater than the y-coordinate of A, so cannot be 5. Whatever it is, the y-coordinate of the orthocenter will be less, so again, your answer fails the reasonableness test.
The perpendicular line to BC through A is ...
... y = (-1/2)(x -2) +6 = -x/2 +7 . . . . . . looks like you had a sign error in (-1/2)(-2)
The intersection of that line and x=6 is ...
... y = -6/2 +7 = 4
the correct option is;
Find the incenter of the triangle
To inscribe a circle in a triangle, we proceed as follows;
1) With the compass, draw the angle bisector of an interior angle of the triangle
2) Construct the angle bisector of a second interior angle of the triangle
3) From the point of intersection of the two angle bisectors which is the incenter of the triangle construct a line perpendicular to one of the sides of the triangle
4) With the compass at the incenter, extend the length to the point of intersection of the perpendicular line and the side of the triangle, then draw the inscribed circle of the triangle.
Therefore, the correct option is to find the incenter of the triangle.
a. acute triangle