Question

please help asap! i need to find the missing coordinate

Answer 1

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.