Question

6. segments r4p and bp have the same length. if the coordinates of a and p are (-1, 0) and (4,l2), respectively, which could be the coordinates of b?

Answer 1

(9,24) and (-8,7) could be the coordinate of B. Hence, the option B is correct.

From the given question,

The segments AP and BP have the same length.

The coordinates of A=(-1, 0) and P=(4,l2).

We have to find the coordinates of B.

let the coordinate of B=(x,y)

So as given:

AP=BP

$\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Putting the values

$\sqrt{(4-(-1))^2+(12-0)^2}=\sqrt{(x-4)^2+(y-12)^2}$

Simplifying

$\sqrt{(4+1)^2+(12)^2}=\sqrt{(x-4)^2+(y-12)^2}$

$\sqrt{(5)^2+(12)^2}=\sqrt{(x-4)^2+(y-12)^2}$

$\sqrt{25+144}=\sqrt{(x-4)^2+(y-12)^2}$

$\sqrt{169}=\sqrt{(x-4)^2+(y-12)^2}$

Square on both side, we get

(x-4)^2+(y-12)^2=169

Now put (3/2,6)

(3/2-4)^2+(6-12)^2=169

{(3-8)/2}^2+(-6)^2=169

(-5/2)^2+36=169

6.25+36=169

42.25=169(false)

Now put (9,24)

(9-4)^2+(24-12)^2=169

(5)^2+(12)^2=169

25+144=169

169=169(True)

Now put (-8,7)

(-8-4)^2+(7-12)^2=169

(-12)^2+(-5)^2=169

144+25=169

169=169(True)

So, (9,24) and (-8,7) could be the coordinate of B.

Hence, the option B is correct.

To learn more about distance formula link is here

brainly.com/question/1633033

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The right question is:

Segments AP and BP have the same lengh. 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