Question

The coordinates of the top of a tree are (-3,8), and an acorn is attached to the tree at (-1,5). If we know that the acorn lies exactly halfway between a squirrel and the top of the tree, what are the coordinates of the squirrel?

Answer 1

(1,2)

Explanation:

By the information given in the problem, we know that the midpoint of the squirrel's coordinates and the tree's coordinates are the coordinates of the acorn on the tree.

Let the squirrel's coordinates be $(x,y)$ so we have $$\left(\frac{-3+x}{2},\frac{8+y}{2}\right)=(-1,5).$$Solving $\frac{-3+x}{2}=-1$ and $\frac{8+y}{2} = 5$, we find that the squirrel's coordinates are $\boxed{(1,2)}$.

Answer 2

Let's say that the coordinates of the squirrel are: (x, y)

Since the coordinates of the acorn is halfway, between the tree and the squirrel, that means the acorn is the midpoint.

To work out the midpoint you do:

(sum of x-coordinates) divided by 2, (sum of y coordinates) divided by 2.

We can use this to form an equation .

So the sum of the x coordinates of the tree and the squirrel = -1 :

x-coordinates of the squirrel:

`(-3+x)/(2)=-1` (now solve for x)

`-3+x = -2`

`x=1`

y-coordinates:

`(8+y)/(2)=5` (now solve for y)

`8+y=10`

`y = 2`

So the coordinates of the squirrel are: (1, 2)

____________________

Answer:

(1, 2)