All categories

2 years ago

Find the coordinates of the orthocenter for XYZ with X(-5,-1) Y(-2,4), Z(3,-1)

Mathematics

1 answer:

V125BC [204]2 years ago

4 0

9514 1404 393

Answer:

(-2, 2)

Step-by-step explanation:

The orthocenter is the intersection of the altitudes. The altitude lines are not difficult to find here. Each is a line through the vertex that is perpendicular to the opposite side.

Side XZ is horizontal, so the altitude to that side is the vertical line through Y. The x-coordinate of Y is -2, so that altitude has equation ...

x = -2

Side YZ has a rise/run of -1/1 = -1, so the altitude to that side will be the line through X with a slope of -1/(-1) = 1. In point-slope form, the equation is ...

y -(-1) +(1)(x -(-5))

y = x +4 . . . . . . . . subtract 1 and simplify

The orthocenter is the point that satisfies both these equations. Using the first equation to substitute for x in the second, we have ...

y = (-2) +4 = 2

The orthocenter is (x, y) = (-2, 2).

You might be interested in

A line passes through the points (-6, 4) and (-2, 2). Which is the equation of the line?

cupoosta [38]

Answer:

$\displaystyle y=-\frac{1}{2}x+1$

Step-by-step explanation:

The equation of any line in slope-intercept form is:

y=mx+b

Being m the slope and b the y-intercept.

Assume we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Two points are given: (-6,4) and (-2,2). Calculating the slope:

$\displaystyle m=\frac{2-4}{-2+6}=\frac{-2}{4}=-\frac{1}{2}$

The equation of the line is, so far:

$\displaystyle y=-\frac{1}{2}x+b$

To calculate the value of b, we use any of the given points, for example (-6,4):

$\displaystyle 4=-\frac{1}{2}(-6)+b$

$\displaystyle 4=3+b$

Solving:

b = 1

The equation of the line is:

$\boxed{\displaystyle y=-\frac{1}{2}x+1}$

We can see none of the choices is correct.

8 0

2 years ago

Find the value of 2 numbers if their sum is 9 and their difference is 1

Sloan [31]

Makes no sense.

p.s i am a fourth grader

5 0

2 years ago

Read 2 more answers

What is the width of a rectangle with length 5.5 cm and area 220 cm^2

Reika [66]

In the given question it is given that the length of the rectangle is 5.5 cm and the area of the rectangle is 220 cm^2.
Length of the rectangle = 5.5 cm
Area of the rectangle = 220 cm^2
Then we already know that
Area of a rectangle = Length * width
So Width of the rectangle = Area of the rectangle/ Length
   = 220/5.5
   = 2200/55
   = 40
So the width of the rectangle is 40 cm.<span>Hope that you have got the answer you were looking for.

</span>

3 0

3 years ago

How can energy be transferred in a car?

kherson [118]

Answer: The internal combustion engine in the car converts the potential chemical energy in gasoline and oxygen into thermal energy which is transformed into the mechanical energy that accelerates the vehicle (increasing its kinetic energy) by causing the pressure and performing the work on the pistons.

Step-by-step explanation: hop this helps

5 0

3 years ago

Read 2 more answers

Please help im desperate. :)

Serhud [2]

D - 6lb / $1 would be the answer

8 0

2 years ago