Question

Determine the distance between the given points. a. \((3,-11),(-12,-3)\) b. \((-7,3),(2,-9)\)

Short answer

Answer: The distance between the points (3,-11) and (-12,-3) is 17 units, and the distance between the points (-7,3) and (2,-9) is 15 units.

Step-by-step solution

a. Find the distance between \((3,-11)\) and \((-12,-3)\).

First, we need to find the difference in x-coordinates and y-coordinates: \(\Delta x = -12 - 3 = -15\) \(\Delta y = -3 - (-11) = 8\) Next, we'll use the distance formula: Distance = \(\sqrt{(\Delta x)^2 + (\Delta y)^2}\) Distance = \(\sqrt{(-15)^2 + (8)^2}\) Distance = \(\sqrt{225 + 64}\) Distance = \(\sqrt{289}\) Distance = 17 So, the distance between the two given points is 17 units.

b. Find the distance between \((-7,3)\) and \((2,-9)\).

First, we need to find the difference in x-coordinates and y-coordinates: \(\Delta x = 2 - (-7) = 9\) \(\Delta y = -9 - 3 = -12\) Next, we'll use the distance formula: Distance = \(\sqrt{(\Delta x)^2 + (\Delta y)^2}\) Distance = \(\sqrt{(9)^2 + (-12)^2}\) Distance = \(\sqrt{81 + 144}\) Distance = \(\sqrt{225}\) Distance = 15 So, the distance between the two given points is 15 units.