Question

The points o, p, q and r all lie on the same line segment, in that order, such that the ratio of o, p, colon, p, q, colon, q, rop:pq:qr is equal to 3, colon, 6, colon, 2, .3:6:2. if o, r, equals, 22, commaor=22, find p, r, .pr.

Answer 1

The value of p, r (pr) is 66 .

Step-by-step explanation:

Given the ratio OP: PQ: QR = 3:6:2, we can express the lengths of the line segments as OP = 3x , PQ = 6x, and QR = 2x , where x is a common multiplier. Now, we are told that OR = 22, which is the sum of OP and PQ since O, P, Q, R are on the same line segment in that order.

OP + PQ = OR

Substitute the values:

3x + 6x = 22

Combine like terms:

9x = 22

Solve for x :

x = 22/9

Now, find PR by adding PQ and QR :

PR = PQ + QR = 6x + 2x = 8x

Substitute the value of x:

PR = 8 × 22/9 = 176/9

Therefore, the value of PR( p, r) is 176/9 or approximately 19.56.

Answer 2

To find PR, we can use the fact that the ratio of the distances is the same as the ratio of the coordinates in the polar coordinate system. Using the given ratio and the distance OR, we can solve for the distance PR.

Step-by-step explanation:

In this problem, we are given the ratio of the distances OP: PQ: QR as 3:6:2. We are also given that the distance OR is 22 units. We need to find the distance PR. To find PR, we can use the fact that the ratio of the distances is the same as the ratio of the coordinates in the polar coordinate system.

Let's denote the distance OP as x. Since the ratio of OP:PQ:QR is 3:6:2, we can write:

OP = 3x, PQ = 6x, QR = 2x

Since OR = OP + PQ + QR, we can substitute the values to get:

22 = 3x + 6x + 2x

Simplifying the equation, we get:

22 = 11x

Dividing both sides by 11, we find that x = 2.

Therefore, the distance PR is PQ + QR = 6x + 2x = 8x = 8 * 2 = 16 units.