Question

Point S
𝑆
is on the circle.

Which correctly shows that point S
𝑆
lies on the circle?

(1 point)
Responses

(3+3)2+(−7+4)2=45
(
3
+
3
)
2
+
(
−
7
+
4
)
2
=
45

(6)2+(−3)2=45
(
6
)
2
+
(
−
3
)
2
=
45

36+9=45
36
+
9
=
45

Table with 1 columns and 3 rows.Row 1: Column 1, 'open paren 3 plus 3 close paren squared plus open paren negative 7 plus 4 close paren squared is equal to 45' Row 2: Column 1, '6 squared plus negative 3 squared is equal to 45' Row 3: Column 1, '36 plus 9 is equal to 45'

(3−3)2+(−7+4)2=9
(
3
−
3
)
2
+
(
−
7
+
4
)
2
=
9

(0)2+(−3)2=9
(
0
)
2
+
(
−
3
)
2
=
9

0+9=9
0
+
9
=
9

Table with 1 columns and 3 rows.Row 1: Column 1, 'open paren 3 minus 3 close paren squared plus open paren negative 7 plus 4 close paren squared is equal to 9' Row 2: Column 1, '0 squared plus negative 3 squared is equal to 9' Row 3: Column 1, '0 plus 9 is equal to 9'

(3−3)2+(−4−7)2=121
(
3

Answer 1

Use the circle equation (x − h)^2 + (y − k)^2 = r^2 with center (−3, −4) and r^2 = 45. For S(3, −7):

(3 − (−3))^2 + (−7 − (−4))^2 = (3+3)^2 + (−7+4)^2 = 6^2 + (−3)^2 = 36 + 9 = 45.

So the first option — (3+3)^2 + (−7+4)^2 = 45 (6^2 + (−3)^2 = 45; 36 + 9 = 45) — correctly shows S lies on the circle.