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Please help asap! i need to find the missing coordinate

Please help asap! i need to find the missing coordinate-example-1
User ZTrix
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1 Answer

1 vote

Answer:

8 or 32

Explanation:

So we are given two coordinates and the length of the segment formed by those coordinates.

To find the unknown coordinate, we can use the distance formula. Let the unknown value be n:

Let's let (-2,n) be x₁ and y₁ and let (-7,20) be x₂ and y₂.

The distance formula is given by the formula:


d=√((x_2-x_1)^2+(y_2-y_1)^2)

Substitute (-2,n) for x₁ and y₁ and (-7,20) for x₂ and y₂. Also, since we already know that the length is 13, substitute it for d. Thus:


(13)=√(((-7)-(-2))^2+((20)-(n))^2)

Do the operations within the parentheses:


13=√((-7+2)^2+(20-n)^2)\\13=√((-5)^2+(20-n)^2)

Now, square both sides to take out the square root:


(13)^2=(√((-5)^2+(20-n)^2))^2

Simplify:


169=(-5)^2+(20-n)^2

Square (-5):


169=25+(20-n)^2

Subtract 25 from both sides. The right cancels:


(169)-25=(25+(20-n)^2)-25\\144=(20-n)^2

Now, take the square root of both sides.


\pm√(144)=√((20-n)^2)

Simplify:


\pm12=(20-n)

So, we have two solutions:


(12=20-n)\text { or }(-12=20-n)

On the left, subtract 20. On the right, also subtract 20:


(-8=-n)\text { or }(-32=-n)

Divide both sides by -1:


(n=8)\text{ or } (n=32)

So, our two possible answers are 8 or 32.

User Zoos
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