Point B has coordinates ​(4,1). The​ x-coordinate of point A is -4. The distance between point A and point B is 10 units. What are the possible coordinates of point​ A?

Answers

Answer 1

Given:

Point B has coordinates ​(4,1).

The​ x-coordinate of point A is -4.

The distance between point A and point B is 10 units.

To find:

The possible coordinates of point​ A.

Solution:

Let the y-coordinate of point A be y. Then the two points are A(-4,y) and B(4,1).

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The distance between point A and point B is 10 units.

[tex]\sqrt{(4-(-4))^2+(1-y)^2}=10[/tex]

Taking square on both sides, we get

[tex](8)^2+(1-y)^2=100[/tex]

[tex](1-y)^2=100-64[/tex]

[tex](1-y)^2=36[/tex]

Taking square root on both sides, we get

[tex](1-y)=\pm \sqrt{36}[/tex]

[tex]-y=\pm 6-1[/tex]

[tex]y=1\mp 6[/tex]

[tex]y=1-6[/tex] and [tex]y=1+6[/tex]

[tex]y=-5[/tex] and [tex]y=7[/tex]

Therefore, the possible coordinates of point​ A are either (-4,-5) or (-4,7).


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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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