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Svet_ta [14]
2 years ago
10

Find the coordinates of the orthocenter of triangle ABC with vertices A (2, 0), B (2, 4), and C (6, 0).

Mathematics
1 answer:
ss7ja [257]2 years ago
8 0

9514 1404 393

Answer:

  (2, 0)

Step-by-step explanation:

The orthocenter of a right triangle is the vertex where the right angle is located. Here, that is vertex A.

The orthocenter is (2, 0).

__

The orthocenter is the point where the altitudes intersect.

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A new library, L, is to be built at some point along a straight road, R, such that its distance from train station, T, is the sh
andreyandreev [35.5K]

Answer:

Coordinates of the new library is (150, 70)

Step-by-step explanation:

To get the shortest possible distance means that line from point T to point R has to be perpendicular.

Now, the equation of R is given as;

y = x - 80 - - - (1)

For T to be perpendicular, it means it will have a slope equal to the negative reciprocal of line R.

Thus, slope of T is -1/1 = - 1

Thus, using line - slope intercept of y = mx + c, we can find equation of T as;

140 = -1(80) + c

140 = -80 + c

c = 140 + 80

c = 220

Thus, equation is;

y = -x + 220 - - - (eq 2)

Adding equation 1 to equation 2,we have;

y + y = 220 - 80

2y = 140

y = 140/2

y = 70

Putting 70 for y in eq 1 gives;

70 = x - 80

x = 70 + 80

x = 150

Thus;

Coordinate of the new library is (150, 70)

8 0
3 years ago
Prove algebraically that r = 10/2+2sinTheta is a parabola
Xelga [282]

Answer:

y =  -  \frac{ 1 }{10} {x}^{2}   +  \frac{5}{2}

Step-by-step explanation:

We want to prove algebraically that:

r =  \frac{10}{2 + 2 \sin \theta}

is a parabola.

We use the relations

{r}^{2}  =  {x}^{2}  +  {y}^{2}

and

y = r \sin \theta

Before we substitute, let us rewrite the equation to get:

r(2 + 2 \sin \theta) = 10

Or

r(1+  \sin \theta) = 5

Expand :

r+  r\sin \theta= 5

We now substitute to get:

\sqrt{ {x}^{2}  +  {y}^{2} }  + y = 5

This means that:

\sqrt{ {x}^{2}  +  {y}^{2} }=5 - y

Square:

{x}^{2}  +  {y}^{2} =(5 - y)^{2}

Expand:

{x}^{2}  +  {y}^{2} =25 - 10y +  {y}^{2}

{x}^{2}  =25 - 10y

{x}^{2}  - 25 =  - 10y

y =  -  \frac{ {x}^{2} }{10}  +  \frac{5}{2}

This is a parabola (0,2.5) and turns upside down.

4 0
3 years ago
Can someone pls help me on the last three!
Solnce55 [7]
Red to total I believe is 12/23
4 0
3 years ago
A basketball player made 80 baskets in a season. Of these, 20% were three-point shots. Determine the number of three-point shots
Amanda [17]
The answer is 16 three-point shots.
The way to do this is by doing 100 / 20 which is 5, and then you would do the total (80) divided by 5 which is 16
8 0
2 years ago
The sum of two number is 50,and their difference is 30.find the numbers​
Mrac [35]

Answer:

40 and 10

Step-by-step explanation:

if you add them you get 50 and if you subtract them you get 30

6 0
2 years ago
Read 2 more answers
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