Question

Point A and Point B are 5 units apart.

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The coordinates of Point A are (-1,2).
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The x-coordinate for Point B is -1.
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What are the possible coordinates for Point B?

Answer 1

`\boxed{\textsf{ The possible values of y is \textbf{ 3 or -3 }.}}`

Explanation:

Here Point A and B are 5 units apart . The coordinates of A are (-1,2) and B is (-1,y) .We need to find the possible coordinates of y . So let's use Distance Formula :-

`\rule{200}2`

★ Distance Formula :-

If we need to find the distance between two points say ,
`\sf ( x_1,y_1 ) \:\:\:\: \& \:\:\:\: ( x_2,y_2)` , then we can find out the distance as ,

`\boxed{\boxed{ \sf Distance =√( ( x_2-x_1)^2+(y_2-y_1)^2 ) }}`

`\rule{200}2`

Put on the respective values ,

`\sf\implies Distance =√( ( x_2-x_1)^2+(y_2-y_1)^2 ) \\\\\sf\implies Distance = √( (-1+1)^2+(2-y)^2)\\\\\sf\implies Distance =√( (2-y)^2 ) \\\\\sf\implies 5^2 = (2-y)^2 \\\\\sf\implies 5 = \pm (2-y) \\\\\sf\implies 5 = (2-y) \qquad or \qquad 5= -(2-y)\\\\\sf\implies y = 2-5 \qquad or \qquad y = 5-2 \\\\\sf\implies\boxed{\pink{\frak{ y = \pm 3 }}}`