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3 years ago

What is the distance between point P and point Q?

Mathematics

1 answer:

kirill115 [55]3 years ago

4 0

Answer:

Option A. half the distance between point A and point K

Step-by-step explanation:

Ax=Fx

Fy=Ky

The distance between point A and point K is:

AK=Ax+Fx+Fy+Ky

Like Ax=Fx and Fy=Ky

AK=Fx+Fx+Fy+Fy

AK=2Fx+2Fy

Common factor 2:

AK=2(Fx+Fy)

The distance between point P and point Q is:

PQ=Fx+Fy

Then the distance between point P and point Q is half the distance between point A and point K:

PQ=Fx+Fy=AK/2=2(Fx+Fy)/2=Fx+Fy

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Find parametric equations which describe each curve. No particular orientation is required.

MA_775_DIABLO [31]

Answer:

The equation of the line is $(x(t),y(t))=(1-4t,2+6t)$ and the equation of the circle is $F(t)= (3cos(t)+4,3sin(t)+1)$ .

Step-by-step explanation:

(a) Given: The given points are $(1,2)$ and $(-3,8)$ .

To find: The parametric equation of line containing points $(1,2)$ and $(-3,8)$ .

We know that the parametric equation of line containing $(x_{1} ,y_{1} )$ and $(x_{2} ,y_{2} )$ is given by $(x(t),y(t))=(x_{1}+(x_{2}-x_{1})t,y_{1}+(y_{2}-y_{1})t)$ where $t$ ∈ $[0,1]$ .

Now, $x(t)=1+(-3-1)t$

i.e, $x(t)=1-4t$

And, $y(t)=2+(8-2)t$

i.e, $y(t)=2+6t$

Hence, the required parametric equation of the line is $(x(t),y(t))=(1-4t,2+6t)$ .

(b) Given: The radius of circle is 3 and centre is $(4,1)$ .

To find: The parametric equation of circle with radius 3 and centre $(4,1)$ .

We know that parametric equation of circle with radius $r$ and centre $(h,k)$ is given by $F(t)= (x(t),y(t))$ where $x(t)=rcos(t)+h$ and $y(t)=rsin(t)+k$ .

Now, $x(t)=3cos(t)+4$

$y(t)=3sin(t)+1$

So, the parametric equation of circle having radius 3 and centre $(h,k)$ is $F(t)= (3cos(t)+4,3sin(t)+1)$ .

Hence, the required equation of the circle is $F(t)= (3cos(t)+4,3sin(t)+1)$ .

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2 years ago

5, 10, 12, 4, 6, 11, 13, 5 calculate the median

leva [86]

Answer:

8 is u r answer dear.

Step-by-step explanation:

just write all the terms in serial order and you'll get two numbers in median 6 and 10 add both and divide it by 2 . That's ur answer !!

Hope you got it.

8 0

2 years ago

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yaroslaw [1]

Answer:

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