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On a coordinate grid, a grocery store is located at (3,0) and the hardware store is located at (4,3). If the pharmacy is the midpoint between the grocery store and the hardware store, what is the approximate distance from the hardware store to the pharmacy? (Note: 1 unit equals 1 mile)

A1.5 miles

B)1.58 miles

C)3.16 miles

D)3.5 miles

E)3.81 miles

Verified Answer :

Tracelate
B1.58 miles. This is because the coordinates (3,0) and (4,3) can be connected to create a right triangle, with side lengths of 1 and 3. Using the Pythagorean theorem, we can determine that the hypotenuse has a distance of 3.16 miles. Because the pharmacy is at the midpoint of this hypotenuse, we can divide the length by 2 and determine the distance from the hardware store to the pharmacy as 1.58 miles.

Midpoint, as the word suggests, means the point which lies in the middle of something. The distance between the hardware store and the pharmacy is 1.5 miles.

What does a midpoint mean?

Midpoint, as the word suggests, means the point which lies in the middle of something. The Midpoint of a line segment means a point which lies in the mid of the given line segment.

The distance between the grocery store and the hardware store can be found by finding the coordinates of the pharmacy,

The coordinates of the pharmacy are,

x = (3+4)/2 = 3.5

y = (0+3)/2 = 1.5

Thus, the coordinates of the pharmacy are (3.5, 1.5).

The distance between the hardware store(4,3) to the pharmacy(3.5, 1.5) can be written as,

\(D = \sqrt{(4-3.5)^2+(3-1.5)^2} = \sqrt{(0.5)^2+(1.5)^2} = 1.5811\rm\ miles\)

Hence, the distance between the hardware store and the pharmacy is 1.5 miles.

Learn more about Midpoint:

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