Question

Please help .... Jeff is traveling from Atlanta to Columbia and then to Charleston. He decides to plot the cities on a coordinate plane. He puts Atlanta at (0, 0), Columbia at (21, 0) and Charleston at (24, -11). He lets each tick mark represent 10 miles. Which formula would correctly solve for the distance from Columbia to Charleston?
A) √24² + (-11)²

B) √24² - 11²

C) √3² + (-11)²

D) √3² - 11²

Answer 1

Answer:

The answer is C

Step-by-step explanation:

Use the Pythagoras theorem which states that a2 = b2 + c 2

For easier understanding imagine a straight line along the x axis. At (0,0) we have Atlanta. Moving 21 units to our right we have Columbia. This is represented on the coordinate system by (21, 0). To go from Colombia to Charleston, which is located at (24, -11), we need to travel 3 units right along the x- axis to reach ‘24’ and ‘11’ units down along the y- axis to reach (24, -11). Starting from Colombia we can make an imaginary triangle with its perpendicular being the y- component and its base being the x- component, which as we have stated above is ‘-11’ and ‘3’ respectively

Now applying the Pythagoras theorem to calculate the hypothesis and hence the distance between Colombia and Charleston.

a, which represents the distance between Colombia and Charleston would be

a² = b² + c²

a² = (3)² + (-11)²

a = √[(3)² + (-11)²]

Hence the answer is C