Question

Point A
𝐴
lies at (2,4)
(
2
,
4
)
and point B
𝐵
lies at (3,6)
(
3
,
6
)
. Which point is needed so that △ABC
△
𝐴
𝐵
𝐶
is isosceles?(1 point)
Responses

C(5,4)
𝐶
(
5
,
4
)
upper C left parenthesis 5 comma 4 right parenthesis

C(3,4)
𝐶
(
3
,
4
)
upper C left parenthesis 3 comma 4 right parenthesis

C(5,5)
𝐶
(
5
,
5
)
upper C left parenthesis 5 comma 5 right parenthesis

C(0,4)

Answer 1

C(5,5).

Reason: AB^2 = (3-2)^2 + (6-4)^2 = 1 + 4 = 5.
For C(5,5), BC^2 = (5-3)^2 + (5-6)^2 = 4 + 1 = 5, so BC = AB and △ABC is isosceles.