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
What is the area of the shaded region?
Mazyrski [523]

Answer:

UINJIBIDHUOSHBIDUNSIUSNIJKDNUHFJDOUUODSJDJSNNSJg

Step-by-step explanation:

5 0
3 years ago
Find s in the parallelogram
adell [148]

Answer:

Step-by-step explanation:

DE=DG

8s-97=3s-22

5s-97=-22

5s=75

s=15

8 0
2 years ago
The quotient of a number x and -1.5 = 21
Lapatulllka [165]

Should be... x ÷ -1.5 = 21

4 0
3 years ago
Read 2 more answers
Direction: Determine whether the given point is a solution to the given system of linear inequalities.
Ann [662]

Answer:

The given point is a solution to the given system of inequalities.

Step-by-step explanation:

Again, we can substitute the coordinates of the given point into the system of inequalities. We know that the x-coordinate and y-coordinate of (3,2) are x=3 and y=2, respectively.

Plugging these values into the first inequality, y\leq x+3, gives us 2\leq 3+3, which simplifies to 2\leq 6. This is a true statement, so the given point satisfies the first inequality. We still need to check if it satisfies the second inequality though, because if it doesn't, it won't be a solution to the system.

Plugging the coordinates into the second inequality, y\geq -x+3, gives us 2\geq -3+3, which simplifies to 2\geq 0. This is also a true statement, so the given point satisfies the second inequality as well. Therefore, \bold(\bold3\bold,\bold2\bold) is a solution to the given system of inequalities since it satisfies all of the inequalities in the system. Hope this helps!

8 0
3 years ago
Please please thank you
nika2105 [10]

Answer:

option 2

452.16

6 0
2 years ago
Read 2 more answers
Other questions:
  • What is 3 multiplied by 3/4?
    9·2 answers
  • Can somebody help me with this question?
    6·2 answers
  • There are 5 marbles in a bag: 4 are blue and 1 is red. What is the probability that a blue marble gets picked?
    8·2 answers
  • PLEASE PLEASE PLEASE PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    13·1 answer
  • A group of tourists go on a tour. the tour guide rents 15 vans. each van holds 9 tourists write a division problem that can be u
    11·1 answer
  • Help! Show your work too plz
    12·1 answer
  • PLS HELP ! Will give brainliest!
    13·1 answer
  • Cam and Madison were investing money into two different accounts. They both invested $550
    8·1 answer
  • Pls help asap no wrong answer pls
    6·2 answers
  • 5 tons of fertilizer cost $6,600.00. What is the price per pound?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!