# Geometry

Find the coordinates of the orthocenter of the triangle with the given vertices.
L (8,0) M (10,8) N (14,0)

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. The orthocentre is the intersection of the altitudes of a triangle.
You will need the equation of two of these and find their intersection

Make a sketch:
notice that LN lies on the x-axis, so the altitude from M is simply x = 10
that was too easy.

let's find the altitude to MN
slope of MN = (8-0)/(10-14) = -2
so slope of altitude is 1/2
and passing through (8,0)
0 = (1/2)(8) + b
b = -4
thus y = (1/2)x - 4
but x = 10
then y = (1/2)(10) - 4 = 1

the orthocentre is (10,1)

As an additional check, find the remaining altitude and verify by subbing in (10,1)

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### Math

Triangle ABC is reflected over the y-axis what are the coordinates of the reflected triangle describe in words what happens to the x coordinates and the y coordinates of the original triangle's vertices as a result of this

2. ### Math 7th

Triangle ABC is shown on the graph below. link to picture a. Triangle ABC is reflected over the y-axis. What are the coordinates of the reflected triangle? b. Describe in words what happens to the x-coordinates and the

3. ### math

triangle abc is reflected over the y-axis. What are the coordinates of the reflected triangle? Describe in words what happens to the x-coordinates and y-coordinates of the original triangle's vertices as a result of this

Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P'Q'R' has vertices P'(1, −2), Q'(0, 3), and R'(−1, 0). Plot triangles PQR and P'Q'R' on your own

1. ### math

Triangle ABC is reflected over the y-axis what are the coordinates of the reflected triangle describe in words what happens to the x coordinates and the y coordinates of the original triangle's vertices as a result of this

2. ### math

Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down. A)Write the coordinated of the vertices of the image after reflection. B)Write a rule for the translation. Use arrow rotation.

3. ### Geometry Unit 7 Lesson 4 Answers

Geometry Unit 7 Lesson 4 Medians and Altitudes This has two parts. The first part is the practice, the second is the quick check. Practice - 9 Questions 1. Which of the following will always pass through a vertex of a triangle?

4. ### math

triangle abc is reflected over the y-axis. What are the coordinates of the reflected triangle? Describe in words what happens to the x-coordinates and y-coordinates of the original triangle's vertices as a result of this

1. ### Math

Triangle ABC has vertices A(–4,–2), B(–1,3), and C(5,0). Triangle ABC is rotated 180° counterclockwise about the origin to form triangle A′B′C′. What are the coordinates of the vertices of the triangle A′B′C′?

2. ### Math

Triangle ABC has vertices A (-4,-2), B (-1,3), and C (5,0). Triangle ABC is rotated 180 degrees counterclockwise about the origin to form triangle A'B'C'. a. what are the coordinates of the vertices of triangle A'B'C'? b. How

3. ### math

A. Triangle ABC is reflected over the y-axis. What are the coordinates of the reflected triangle? B. Describe in words what happens to the x-coordinates and y-coordinates of the original triangle’s vertices as a result of this

4. ### Geometry

The coordinates of the vertices of CDE are C(1, 4), D(3, 6), and E(7, 4). If the triangle is reflected over the line y = 3, what are the coordinates of the image of D?