1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
r-ruslan [8.4K]
3 years ago
10

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

Mathematics
1 answer:
V125BC [204]3 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
I need help on this one thanks!!
mart [117]

Answer:

CU = 12

Step-by-step explanation:

Clearly from the diagram of the triangle we can say that,

AD, BE and CF are the medians of the triangle ABC , since they are bisecting the sides of the triangle equally.

Also , U is the intersection point of the these mediands of the triangle whic is known as centroid of the triangle.

Now, from the property of the centroid , centroid divides the median in the ratio of 2 :1 from the point C .

Thus CU will be \frac{2}{3} times of CF (median) .

Given is Cf equals 18 ,

Thus , CU = \frac{2}{3}×18 = 12.

So, CU equals 12 .

8 0
3 years ago
A plane ticket to Barcelona costs £175
Advocard [28]

Answer:

Given:

A plane ticket to Barcelona costs £175 the price decreases by 6%

To find:

The new price of the plane ticket

Solution:

The ticket to Barcelona costs £ 175

The price decreases by 6%

⇒ 6% = 6/100 = 3/50

The new price of the plane ticket is decreased by the amount,

= £ 175 × 3/50

= £ 10.5

Therefore, the new price of the plane ticket is given by,

= £ 175 - £ 10.5

= £ 164.5

ik this question i got at school

7 0
2 years ago
Read 2 more answers
A student reading his physics book on a lake dock notices that the distance between two incoming wave crests is about 2.4 m and
mojhsa [17]

Answer:

v=2.4/1.6=1.5 m/s

Hope it helps

Have a good day

4 0
3 years ago
. Ethan's favorite kind of exercise is running. He runs on a path that is 1.75 miles long. Last week, Ethan ran on the path 6 ti
Talja [164]

Answer:

10.5 miles

Step-by-step explanation:

Ethan's favorite kind of exercise is running. He runs on a path that is 1.75 miles long. Last week, Ethan ran on the path 6 times.

The number of miles that Ethan ran on the path last week is calculated as:

Number of miles × Number of times he ran

= 1.75 miles × 6 times

= 10.5 miles

Therefore, the number of miles that Ethan ran on the path last week is 10.5 miles

6 0
2 years ago
A 45-45-90 triangle has a hypotenuse of length 7. What is the length of one of its legs? If necessary, round your answer to two
harkovskaia [24]
If the legs are legnth x, then the hyptonuse is x√2

x√2=7
divide both sides by √2
x=7/√2
times (√2)/(√2)
(7√2)/2
3.5√2
aprox 4.94974
round
4.95
4 0
3 years ago
Other questions:
  • What is the length of the unknown leg in the right triangle?
    10·2 answers
  • Which number is not divisible by either of the numbers three and five?
    6·2 answers
  • A snake dives toward deeper water at a rate of 10 inches per second. If the snake continues at this speed for 7 seconds, which e
    15·2 answers
  • Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0 beats per minute and a standard
    11·1 answer
  • Simplify: –4(x – 2) – 5(y + 2) + (–3)(8 – 6b)
    8·2 answers
  • What is the solution of the inequality<br> -6x-17greater or equal to 8x+25
    7·2 answers
  • Use the binomial theorem to expand the binomial(simple steps).<br> (d-4b)^3<br> Urgent help needed
    7·1 answer
  • Simplify the algebraic expression 8y-2(y+4)
    6·2 answers
  • Multiply. Write your answer as a mixed number in simplest form.
    5·1 answer
  • Please help me one this someone please!!!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!