Question

On the coordinate grid of a map, Josie's house is located at ( 2 , 7 ). Her school is located at ( -5 , 5 ). If each map unit equals one mile, what is the approximate distance from her house to her school?

A) 2.83 miles
B) 4.79 miles
C) 7.28 miles
D) 12.37 miles

Answer 1

Answer: C) 7.28 miles

Explanation:

Given: On the coordinate grid of a map, Josie's house is located at ( 2 , 7 ). Her school is located at ( -5 , 5 ).

Using distance formula ,distance between points (a,b) and (x,y) is :

`d=√((x-a)^2+(y-b)^2)`

Now, distance from her house to her school ia given by :-

`d=√((-5-2)^2+(5-7)^2)\\\\=√((-7)^2+(-2)^2)\\\\=√(49+4)\\\\=√(53)=7.28010988928\approx7.28\text{ miles}`

Hence, the approximate distance from her house to her school = 7.28 miles

Answer 2

Option C.
`7.28\ miles`

Explanation:

we know that

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Let

`A(2,7)\\E(-5.5)`

substitute the values

`d=\sqrt{(5-7)^(2)+(-5-2)^(2)}`

`d=\sqrt{(-2)^(2)+(-7)^(2)}`

`d=√(53)\ units`

Remember that

each map unit equals one mile

so

`√(53)\ units=√(53)\ miles=7.28\ miles`