Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form.
left bracket, minus, 2, comma, 4, right bracket, and , left bracket, minus, 7, comma, minus, 8, right bracket
(−2,4) and (−7,−8)
leg 1:
leg 2:
hypotenuse:
To find the distance between the two points, we can use the distance formula:
Distance = √( (x2 - x1)^2 + (y2 - y1)^2 )
Using the points (-2, 4) and (-7, -8):
leg 1: x2 - x1 = -7 - (-2) = -7 + 2 = -5
y2 - y1 = -8 - 4 = -12
leg 2: x2 - x1 = -7 - (-2) = -7 + 2 = -5
y2 - y1 = -8 - 4 = -12
Distance = √((-5)^2 + (-12)^2)
= √(25 + 144)
= √169
= 13
The distance between the two points is 13.