Line segment PQ has endpoints P(7,11) and Q(15,21) and is the diameter of a circle.
a) Determine the centre of the circle.
I know you use the Midpoint formula for this question.
b) Calculate the radius of the circle to the nearest tenth of a unit.
This is the one that really threw me off. Would you use the distance formula for x1 and x2 & y1 and y2 to figure out the diameter, and then divide by two?
2006-11-20 13:06:54 · 6 answers · asked by astro_dj 2 in Science & Mathematics ➔ Mathematics
(a) By drawing the points on a graph sheet, Midpoint is determined as (11,16)
(b) Again by drawing on a graph sheet, by using Hypotenuse theorem;
Radius = Longest side of right angled triangle
= square root of (4^2+5^2)
= square root of (16+25)
= square root of (41)
= 41^0.5
= 6.4
2006-11-20 13:30:45 · answer #1 · answered by ShashiSG 2 · 0⤊ 0⤋
a) Yes, the midpoint would be 11,16.
b) I've been out of school for a long time and don't remember all the methods they teach (and they probably changed), but the easiest way to figure this out would be to construct a right triangle with the line segment as the hypotenuse. It sounds like this is what you may be trying to do, or you at least have part of it.
The line segment parallel to the x-axis would go from 7,11 to 15,11 and have a length of 8. The line segment parallel to the y-axis would go from 15,11 to 15,21 and have a length of 10. So you now have a right triangle, where the line segment between P and Q is the hypotenuse.
You would use the pythagorean theorem to get the hypotenuse, a^2 + b^2 = c^2, where c is the hypotenuse (and also the diameter of the circle). So:
8^2 +10^2 = c^2
64+100 = c^2
164 = c^2
c=12.806248... (approximately)
Therefore, the radius is c/2 = 6.4, rounded to the nearest tenth.
2006-11-20 13:32:35 · answer #2 · answered by Alan S 6 · 0⤊ 0⤋
a.)
Mx = (7 + 15)/2 = 22/2 = 11
My = (11 + 21)/2 = 32/2 = 16
ANS : (11,16)
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b.)
You don't actually need to do that, Just use the midpoint and one of the previous points.
D = sqrt((15 - 7)^2 + (21 - 11)^2)
D = sqrt(8^2 + 10^2)
D = sqrt(64 + 100)
D = sqrt(164)
D = sqrt(4 * 41)
D = 2sqrt(41)
2006-11-20 16:00:16 · answer #3 · answered by Sherman81 6 · 0⤊ 0⤋
b. Yes that is correct. Or you can just use the formula with one point from the question and the midpoint you found.
2006-11-20 13:08:55 · answer #4 · answered by jacinablackbox 4 · 0⤊ 0⤋
That seems like the most suitable answer, especially if it says nearest tenth of a unit. =)
2006-11-20 13:09:42 · answer #5 · answered by x_moonlightshine 2 · 0⤊ 0⤋
YES
2006-11-20 13:23:11 · answer #6 · answered by Math Geek 2 · 0⤊ 0⤋