To find the distance between two points in a Cartesian plane, you can use the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
a. For the points (-8, -2) and (6, -1):
x1 = -8
y1 = -2
x2 = 6
y2 = -1
Distance = √[(6 - (-8))² + (-1 - (-2))²]
Distance = √[(6 + 8)² + (-1 + 2)²]
Distance = √[14² + 1²]
Distance = √(196 + 1)
Distance = √197
So, the distance between (-8, -2) and (6, -1) is √197 units.
b. For the points (-4, 5) and (4, 0):
x1 = -4
y1 = 5
x2 = 4
y2 = 0
Distance = √[(4 - (-4))² + (0 - 5)²]
Distance = √[(4 + 4)² + (0 - 5)²]
Distance = √[8² + (-5)²]
Distance = √(64 + 25)
Distance = √89
So, the distance between (-4, 5) and (4, 0) is √89 units.