Question

what is the length of the line?
choose 1 answer:
a 9
b 8
c $sqrt{45}$
d $sqrt{27}$

Explanation:

Step1: Determine horizontal and vertical distances

Count the horizontal \( \Delta x\) and vertical \( \Delta y\) distances between the endpoints of the line. Here, \( \Delta x = 6\) and \( \Delta y = 3\).

Step2: Apply the distance formula

The distance formula is \( d=\sqrt{(\Delta x)^2+(\Delta y)^2}\). Substitute \( \Delta x = 6\) and \( \Delta y = 3\) into the formula: \( d=\sqrt{6^{2}+3^{2}}=\sqrt{36 + 9}=\sqrt{45}\).

Answer:

C. \(\sqrt{45}\)