Question

ABC has vertices A(0, 6), B(4, 6), and C(1, 3). Sketch a graph of ABC and use it to find the orthocenter of ABC. Then list the steps you took to find the orthocenter, including any necessary points or slopes you had to derive.

Answer 1

is there a image

Answer 2

no

Answer 3

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Kd6009886
no
\(\color{#0cbb34}{\text{End of Quote}}\)
ok well I can't help without and image

Answer 4

Here is another way to do it: vector approach.

Since AB is a horizonal line, the altitude through C must be a vertical line. So, the orthocenter coordinates can be written as (1, b), and the direction of the altitude from A is (1, b-6), and the direction of BC is parallel to (1, 1). Since the dot product of two perpendicular vector is zero, we have

(1, b-6) ⋅ (1, 1) = 0

1 + b-6 = 0

b = 5

Answer: The orthocenter is at (1, 5).