P(-,3) , Q(7,-3) and R (4,1) are three points. show that PQ=2QR using distance formula. (please show the steps too :)

PQ is 10.

QR is 5.

Hence, PQ=2QR

Step-by-step explanation:

We have the three points P(-1, 3); Q(7, -3); and R(4, 1).

And we want to show that PQ=2QR.

In other words, we want to show that PQ/QR=2.

So, let's find PQ and QR. We will need to use the distance formula:

To find PQ:

P is (-1, 3) and Q is (7, -3).

So, we will let P(-1, 3) be (x₁, y₁) and Q(7, -3) be (x₂, y₂).

Substitute the values into the distance formula. This yields:

Evaluate:

Evaluate:

So, the distance of PQ is 10.

And to find QR:

Q is (7, -3) and R is (4, 1).

Again, we will let Q(7, -3) be (x₁, y₁) and R(4, 1) be (x₂, y₂).

Substitute appropriately. So:

Evaluate:

Evaluate:

So, the distance of QR is 5.

Therefore, it follows that:

And we have shown that PQ=2QR.

the answer

b. they are parallel and will never intersect.

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.