Question

m = (2, 5)
n = (-4, -5)
o = (-2, 4)
p = (-2, -1)

Explanation:

Step1: Identify the problem type

This problem involves finding the distance between two points or analyzing the slope of a line between two points, which falls under the subfield of Algebra (specifically coordinate geometry) in Mathematics. Let's assume we need to find the distance between points M(2, 5) and N(-4, -5), or between O(-2, 4) and P(-2, -1).

Step2: Recall the distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Step3: Calculate distance for M and N

For points M(2, 5) and N(-4, -5):
\(x_1 = 2\), \(y_1 = 5\), \(x_2 = -4\), \(y_2 = -5\)
\(d = \sqrt{(-4 - 2)^2 + (-5 - 5)^2} = \sqrt{(-6)^2 + (-10)^2} = \sqrt{36 + 100} = \sqrt{136} = 2\sqrt{34} \approx 11.66\)

Step4: Calculate distance for O and P

For points O(-2, 4) and P(-2, -1):
\(x_1 = -2\), \(y_1 = 4\), \(x_2 = -2\), \(y_2 = -1\)
\(d = \sqrt{(-2 - (-2))^2 + (-1 - 4)^2} = \sqrt{(0)^2 + (-5)^2} = \sqrt{0 + 25} = \sqrt{25} = 5\)

Answer:

If the question was about the distance between O and P, the answer is 5. If it was about M and N, the answer is \(2\sqrt{34}\) (or approximately 11.66). Based on the "5" written in the image, likely the distance between O and P is 5.