Chapter 1: Orienting Yourself: The Use of Coordinates
Chapter 1: Orienting Yourself: The Use of Coordinates
Exercise
Question
Question: 12 (ii)
19 / 25
19 / 25
(ii) Given the points D (-5, 6) and E (0, 9), check whether D and E lie within the circle, on the circle, or outside circle K.
SponsoredDesktop Banner
Answer
1
Find the distance of D and E from the origin.
\text{OD = $\sqrt{(0 - (-5))^2 + (0 - 6)^2} = \sqrt{5^2 + (-6)^2} = \sqrt{25 + 36} = \sqrt{61}$}
\text{OE = $\sqrt{(0 - 0)^2 + (0 - 9)^2} = \sqrt{0^2 + (-9)^2} = \sqrt{0 + 81} = \sqrt{81} = 9$}
2
Compare the distances OD and OE with the radius of circle K, \sqrt{65}. A point lies inside the circle if its distance from the centre is less than the radius, on the circumference if the distance equals the radius, and outside the circle if the distance is greater than the radius.Note: From part (i), the radius of circle K is \sqrt{65} \simeq 8.1.
Answer: D is inside circle K, while E is outside circle K.
\textbf{Reason: OD = $\sqrt{61}$, which is less than the radius $\sqrt{65}$. Therefore, D lies inside circle K. OE = 9, which is greater than the radius $\sqrt{65}\ (\simeq 8.1)$. Therefore, E lies outside circle K.}