Question

A triangle has angles (-3,5) (6,5) (0,-1) what is the point of intersection of its altitudes

Answer 1

they wanna know the height

Answer 2

Ya the intersection of the lines of height of all three sides

Answer 3

hello edsgirl17, have you taken up dot products already? It can be solved using such.

Answer 4

no I haven't I am supposed to use slope midpoint and y=mx+ b to find it

Answer 5

The point of intersection of the altitudes of a triangle is called the orthocentre.

An altitude of a triangle is a line segment produced from a vertex and is perpendicular to the opposite side.

To find the orthocentre algebraically, find the equations of any two altitudes and find their points of intersection.

To find the equation of an altitude from a vertex,
i). find the slope of the side opposite the vertex, and the negative reciprocal of this slope is the slope of the altitude.

ii). Using this slope and the vertex from which the altitude is produced, find the equation of the altitude.

Repeat the above steps to find the equation of the altitude from another vertex, and then using the method of substitution or elimination, find the orthocentre.


Now try to solve the problem, and let me know if you need further assistance.

Answer 6

Thanks @calculusfunctions I have been following those steps the problem is the final x value always ends up as zero and then I don't know how to find the y value before I use substitution

Answer 7

Your question:

Given ΔABC, A(-3, 5), B(6, 5) and C(0,-1).

We may choose to find the altitudes from any two of the three vertices. Let's suppose we choose vertices A and C.

I). Find the equation of the altitude from vertex A.
Opposite side is then BC. Thus

slope m of BC = (-1 − 5)/(0 − 6)

slope m of BC = 1

Thus the slope of the altitude from vertex A is -1

Now using the slope of the altitude m = -1 and the vertex A(-3, 5),

y = mx + b

5 = (-1)(-3) + b

5 = 3 + b

b = 2

Thus the equation of the altitude from vertex A is y = -x + 2.


II). Find the equation of the altitude from vertex C.
Opposite side is AB.

slope m of AB = (5 - 5)/(6 − -3)

slope m of AB = 0

Thus the slope of the altitude from vertex C is undefined. This implies that the altitude from vertex C is a vertical line. The equation of any vertical line is x = k where k is the x-coordinate of any point on the vertical line. Since the x-coordinate of vertex C is 0, the equation opf the altitude from vertex C is x = 0.

Substitute x = 0 into the equation of the altitude from vertex A, y = -x + 2, to obtain

y = 2

∴ the point of intersection of the altitudes is (0, 2). In other words the orthocentre of ΔABC lies at (0, 2).

Let me know if you understand or if you need clarification on anything I've said.

Answer 8

^copied and pasted from textbookanswers.com

Answer 9

What was copied and pasted?

Answer 10

It was a joke. There is no such site. Maybe I should purchase the domain.

Answer 11

Oh LOL!

Answer 12

calculusfunctiions i need help in the MIT prob set!

Answer 13

bbnl1990, I have to log off now but when I return. Unless it's quick. Can you tell me what you need?

Answer 14

OMG THANK YOU SOO MuCH @calculusfunctions