Question

Segments AP and BP have the same length. If the coordinates of A and P are (-1,0) and (4,12), respectively, which could be the coordinates of B?

I. (3/2, 6)

II. (9, 24)

III. (-8,7)


A) I and II only

B) II and III only

C) II only

D) III only

Answer 1

B) II and III only

Explanation:

Coordinates of A = (-1,0)

Coordinates of P =(4,12)

Let (x,y) be the coordinates of B

Distance formula : =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

AP = BP

`√((4+1)^2+(12-0)^2)=√((4-x)^2+(12-y)^2)`

`(4+1)^2+(12-0)^2=(4-x)^2+(12-y)^2`

`169=16+x^2-8x+144+y^2-24y`

`x^2-8x+y^2-24y-9=0`

I)(3/2,6)

`((3)/(2))^2-8((3)/(2))+6^2-24(6)-9=0\\-126.75 \\eq 0`

II)(9,24)

`(9)^2-8(9)+(24)^2-24(24)-9=0`

0= 0

C)(-8,7)

`(-8)^2-8(-8)+(7)^2-24(7)-9=0`

0=0

So, II and III could be the coordinates of B

So Option B is true

II) II and III only