Question

is the diameter of a circle with center P. The coordinates of the endpoints of the diameter are (1, 3) and (6, 6). What are the coordinates of P?


A) (2, 6)
B) (2.2, 3)
C) (2.5, 3.5)
D) (4.5, 5)
E) (3.5, 4.5)

Answer 1

@mathslover , can yooou help?(:

Answer 2

The centre P will lie in between the diameter, right?

Answer 3

yes, I think

Answer 4

Since, radius = half of diameter

So, AP = AB/2

Thus, basically, P will lie exactly in between those two points.

So,

Answer 5

Now, remember this :

Coordinates of a point P lying between two points A and B such that AP = BP = AB/2

Then :

\(P \equiv \left( \cfrac{x_1 + x_2 }{2} , \cfrac{y_1+ y_2}{2} \right)\)

Where : \(A \equiv (x_1 , y_1)\) and \(B \equiv (x_2 , y_2)\)

Answer 6

Here, you have \(A \equiv (1,6)\) and \(B\equiv (6,6)\)

So, just plug-in these values in the equation I gave above. And find the coordinates of P.

Answer 7

I got 3.5, and 6..which is not one of the answer choices!

Answer 8

3.5 is correct ! Please recheck your process. You might have done a mistake in calculation.