Question

1-2) Find the distance between (2, 6) and (7,-2), and find the midpoint of a line

connecting those points. (You do not need to simplify the radical for the distance.)

Answer 1

Explanation:

the x and y coordinate differences of 2 points create a right-angled triangle, with the curvy distance being the Hypotenuse.

so, we can use Pythagoras to get the distance

c² = a² + b²

c being the Hypotenuse, a and b being the legs.

distance² = (2 - 7)² + (6 - -2)² = (2 - 7)² + (6 + 2)² =

= (-5)² + 8² = 25 + 64 = 89

distance = sqrt(89)

given 2 points

(x1, y1)

(x2, y2)

the midpoint is

((x1 + x2)/2, (y1 + y2)/2)

so, our midpoint is

((2+7)/2, (6-2)/2) = (9/2, 4/2) = (4.5, 2)