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grigory [225]
3 years ago
6

Please help asap! i need to find the missing coordinate

Mathematics
1 answer:
Harrizon [31]3 years ago
5 0

Answer:

8 or 32

Step-by-step 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=\sqrt{(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)=\sqrt{((-7)-(-2))^2+((20)-(n))^2}

Do the operations within the parentheses:

13=\sqrt{(-7+2)^2+(20-n)^2}\\13=\sqrt{(-5)^2+(20-n)^2}

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

(13)^2=(\sqrt{(-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\sqrt{144}=\sqrt{(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.

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