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
murzikaleks [220]
3 years ago
9

Find the coordinates of the orthocenter of ΔYAB that has vertices at Y(3, –2), A(3, 5), and B(9, 1).

Mathematics
1 answer:
just olya [345]3 years ago
5 0

Answer:

(5,1)

Step-by-step explanation:

The orthocenter will be the intersection of the altitudes.

The altitudes are found by drawing from a vertex of the triangle to the opposite side such that the line segment you draw is perpendicular the line segment it intersects with.

The most obvious equation is the one from from vertex B to side AY which y=1 (the purple one).  

So we already know the y-coordinate has to be 1.

If we are able to find one of the other equations we can find the corresponding x of the intersections there.

Let's look at the green one; the line drawn from vertex Y to side AB.  

So let's find the equation for this line.

We know it has point (3,-2) and that is is perpendicular to the line AB.

So we know that perpendicular lines have opposite reciprocal slopes so we will need to start with finding the slope of AB to obtain the slope of our altitude formed by vertex Y and side AB.

So A is at (3,5) and B is (9,1)

To find the slope, I'm going to line up the points vertically and subtract, then put 2nd difference over 1st difference.

(9 , 1)

-(3 , 5)

-----------

6    -4

The slope of AB is -4/6 or -2/3 after reducing (divided top and bottom by 2 to obtain this reduction).

The opposite reciprocal of -2/3 is 3/2.

So the slope of the equation that is in green is 3/2 and it goes through point (3,-2).

I'm going to use point-slope form to find the line.

y-y_1=m(x-x_1) is called point-slope form because (x_1,y_1) is a point on the line and m is the slope.

Let's plug in the information we have:

y-(-2)=\frac{3}{2}(x-3)

y+2=\frac{3}{2}(x-3)

The system of equations we want to solve is:

y+2=\frac{3}{2}(x-3)

y=1

I'm going to substitute 1 for y in the first equation since y=1:

y+2=\frac{3}{2}(x-3)

1+2=\frac{3}{2}(x-3)

3=\frac{3}{2}(x-3)

If you don't like the fraction multiply both sides by 2 to obtain:

6=3(x-3)

Divide both sides by 3:

\frac{6}{3}=\frac{3(x-3)}{3}

Simplify:

2=x-3

Add 3 on both sides:

x=5

So the orthocenter is at (x,y)=(5,1)

I drew the drawing below just to show you what this looks like.

I actually drew this drawing before doing the math.  I tried to draw the line segments from a vertex to an opposite side so that the angle formed from my line segment I drew to the opposite side was perpendicular (meaning forming 90 degree angles).

You might be interested in
Peter is wants to lose weight. He is105Kg. His aim is to lose 500 g Per week. If he managed this, how many weeks will it be unti
natali 33 [55]

105 - 90 = 15kg

500g = 1/2 kg

Peter is 15kg overweight.

15 x 2 = 30

It will take him 30 weeks for this.

8 0
3 years ago
What is extended form for 76.429
Zanzabum
(70x10)+(6x1)+(4x1/10)+(2x1/100)+(9x1/1000)
3 0
3 years ago
Can anyone help me with this question?
victus00 [196]
It is a

That the answer
3 0
2 years ago
A function is expressed by the equation y=0.3x−6. For what value of the independent variable will the value of the function be e
Anna11 [10]

Answer:

0; 10; 20

Step-by-step explanation:

x is the independent variable

y is the dependent variable

y is dependent on x

a) For what value of the independent variable will the value of the function be equal to −6

y=0.3x−6

-6 = 0.3x-6

0=0.3x

x = 0

Therefore, if the independent variable is 0, the value of the function will be -6.

b) For what value of the independent variable will the value of the function be equal to −3

y=0.3x−6

-3 = 0.3x-6

0.3x = -3+6

0.3x = 3

x = 3/0.3

x = 10

Therefore, if the independent variable is 10, the value of the function will be -3.

c) For what value of the independent variable will the value of the function be equal to 0.

y=0.3x−6

0=0.3x-6

6 = 0.3x

x = 6/0.3

x = 20

Therefore, if the independent variable is 20, the value of the function will be 0.

7 0
3 years ago
A diamond shaped sign is a ______ sign
suter [353]

A warning/caution sign?

7 0
3 years ago
Other questions:
  • 3 lb 5 oz X 6 = __lb __ oz
    7·1 answer
  • Cleo wants to jion a gym. There is an initiation fee of $24.99, and each month of membership costs $12.50. If Cleo pays $174.99,
    11·1 answer
  • Monica won 7 of the 16 science competitions she entered. To the nearest thousandth, find her wining average.
    8·2 answers
  • You can remember the three numbers to your combination lock, but you can't remember their order. How many different combinations
    15·2 answers
  • How to find the average<br> of 78, 79, 87, 88, 101, 120, 130
    11·2 answers
  • If you miss a payment for a bill, how do you compute the interest due on the next bill?
    11·2 answers
  • What is the slope of the line through (2,-2) and (9,3)?'
    15·1 answer
  • Which is the graph of y=-x-3?
    8·1 answer
  • Help i need your help with this
    7·2 answers
  • Which values should you plot to show a linear relationship?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!