Respuesta :
Answer: Amit's mistake : The point (2, –2) doesn’t lie on the circle because the calculated distance should be the same as the radius.
Step-by-step explanation: Given center of the circle (-1,2) and diameter 10 units and a point (2,-2).
Radius of the circle is half of the diameter.
So, the radius = 10/2 = 5.
Therefore, first step Amit applied is correct.
Second step is also correct to check if the distance between center (-1,2) and given point (2,-2) is same as length of radius.
Let us check what is the distance between enter (-1,2) and given point (2,-2).
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]=\sqrt{\left(2-\left(-1\right)\right)^2+\left(-2-2\right)^2} =\sqrt{25} =5[/tex]
In third step, Amit didn't find equal distance between center (-1,2) and given point (2,-2) same as radius 5.
But it is same.
Therefore, Amit did some mistake in 3rd step.
Amit's work is not correct given that he did not calculate correctly for the distance. Third option.
Why Is Amit's work wrong?
To determine this, we would have to solve for the distance of the circle.
This is given as:
[tex]\sqrt{(y2-y1)^2+(x2-x1)^2} \\\\\sqrt{(-2-2)^2+(2--1)^2}[/tex]
D = √16 + 9
D = √25
D = 5
Given that the distance between the coordinate same as the circle's radius the coordinate (2, -2) lies on the circle.
We have to conclude that Amit is wrong since he did not calculate the distance correctly.
complete question:
Is Amit's work correct? No, he should have used the origin as the center of the circle. No, the radius is 10 units, not 5 units. No, he did not calculate the distance correctly. Yes, the distance from the center to (2, –2) is not the same as the radius.
Read more on distance here: https://brainly.com/question/18522970?referrer=searchResults
