Question

Please help asap! i need to find the missing coordinate

Answer 1

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.