Question

mathematics progress check
so, (-8,5) is on circle a.
kathy

4 - (-2)	+	-1 - 3	= 10
-8 - (-2)	+	7 - 3	= 14

so, (-8,7) is not on circle a.
so, (2,-3) is on circle a.
mason

4 - (-2)	+	-1 - 3	= 10
3 - (-2)	+	-2 - 3	= 10

so, (3,-2) is on circle a.
which student correctly evaluated whether their assigned point was on circle a?
a. theresa
b. blair
c. kathy
d. mason

Explanation:

Step1: Recall the distance - formula for a circle

The general way to check if a point $(x,y)$ is on a circle with center $(h,k)$ is to use the distance formula $d=\sqrt{(x - h)^2+(y - k)^2}$. Here, it seems the students are using a non - standard way (sum of absolute differences). But we can analyze their calculations. Let's assume the center of circle $A$ is $(-2,3)$.

Step2: Analyze Kathy's work

For Kathy:
The first calculation $|4-(-2)|+|-1 - 3|=|6|+|-4|=6 + 4=10$.
The second calculation for the point $(-8,7)$: $|-8-(-2)|+|7 - 3|=|-6|+|4|=6 + 4=10$. Since she got a different value for the second point's calculation compared to the first one (assuming the circle has a consistent property for points on it), her method is inconsistent.

Step3: Analyze Mason's work

For Mason:
The first calculation $|4-(-2)|+|-1 - 3|=|6|+|-4|=10$.
The second calculation for the point $(3,-2)$: $|3-(-2)|+|-2 - 3|=|5|+|-5|=5 + 5=10$. He has consistent results for different points, which implies that if the correct method for this circle is the sum of absolute differences being a constant value for points on the circle, Mason's evaluation is correct.

Answer:

D. Mason