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

Step-by-step 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 :

$d=\sqrt{(x-a)^2+(y-b)^2}$

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

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

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

Answer 2

Answer:

Option C. $7.28\ miles$

Step-by-step 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

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

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

$d=\sqrt{53}\ units$

Remember that

each map unit equals one mile

so

$\sqrt{53}\ units=\sqrt{53}\ miles=7.28\ miles$