Question

question
what is the distance between the points (10, 12) and (-4, -36)?
standard(s)
nc.8.g.8: apply the pythagorean theorem to find the distance between two points in a coordinate system.
other questions on this standard: 1, 2
answer
a 14 units
b 22 units
c 48 units
d 50 units

Explanation:

Step1: Find the differences in coordinates

Let \((x_1,y_1)=(10,12)\) and \((x_2,y_2)=(-4,-36)\).
\(\Delta x=x_2 - x_1=-4 - 10=-14\), \(\Delta y=y_2 - y_1=-36 - 12=-48\).

Step2: Apply the distance formula \(d = \sqrt{(\Delta x)^2+(\Delta y)^2}\)

\(d=\sqrt{(-14)^2+(-48)^2}=\sqrt{196 + 2304}=\sqrt{2500}\).

Step3: Simplify the square - root

\(\sqrt{2500}=50\).

Answer:

D. 50 units