Question

I’m confused on this one

Answer 1

The orthocenter in a triangle is where all the different altitudes intersect. To find this, you would have to take a point, and the line opposite it, and find the line that goes through the point and is perpendicular to the line, and then find one for a different point, set up a system of equations, and solve.

A (-3, -2) B (-2, 2) C (2, -2)

The equation for the line BC is y = -x + 0. The point opposite this line is A.

The equation for a perpendicular line to y = -x + 0 is y = x + 0. We then have to fit this equation to go through point A, so -2 = -3 + 1, so y = x + 1.

Repeating this process with B and line AC gives us the equation x = -2.

Setting up a system of equation will give us the result.

y = -2 + 1

y = -1

x = -2

The point would be (-2, -1)

Answer 2

The orthocenter is the point where all the altitudes intersect. Since they all intersect there, any two altitudes will show you the position of the orthocenter. It can be helpful for problems like this to draw a diagram to scale.

In your triangle, line AC is horizontal, so the altitude through point B will be the vertical line x=-2.

Line BC has a slope of -1, so the altitude through point A will have a slope of the negative reciprocal of that, -1/-1 = 1. Since point A is 1 unit left of x=-2, the orthocenter will be 1 unit up from y=-2.

The appropriate answer is the point (-2, -1).