We have been given that Layana’s house is located at $(2\frac{2}{3}, 7\frac{1}{3})$ on a map. The store where she works is located at $(-1\frac{1}{3}, 7\frac{1}{3})$ .

We are asked to find the distance from Layana’s home to the store

We will use distance formula to solve our given problem.

Let us convert our given coordinates in improper fractions.

$2\frac{2}{3}\Rightarrow \frac{8}{3}$

$7\frac{1}{3}\Rightarrow \frac{22}{3}$

$-1\frac{1}{3}\Rightarrow -\frac{4}{3}$

Now we will use distance formula to solve our given problem.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Upon substituting coordinates of our given point in above formula, we will get:

$D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}$

$D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}$

$D=\sqrt{0+(\frac{8+4}{3})^2}$

$D=\sqrt{(\frac{12}{3})^2}$

$D=\sqrt{(4)^2}$

$D=4$

Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.

3 0

3 years ago

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the perimeter of a rectangular field is (16a+8b-6c) units and one of its side is (5a+3b-4c) find the other side

Jet001 [13]

3a+b+c

The perimeter is two times one side (to account for the opposite) and two times the adjacent side. So if the sides would be x and y, the perimeter would be 2*x + 2*y.

So, knowing that the sum is 16a+8b-6c, if we subtract the given side 5a+3b-4c from this, what remains is two times the "other" side:

16a+8b-6c - 2*(5a+3b-4c) =

16a+8b-6c -10a-6b+8c =

6a+2b+2c

half of that is

(6a+2b+2c)/2 = 3a+b+c

7 0

3 years ago