Question

What is the distance between the points 4 comma 9 and 1 comma 3?

Answer options with 4 options
A.
StartRoot 18 EndRoot

B.
StartRoot 27 EndRoot

C.
StartRoot 29 EndRoot

D.
StartRoot 45 EndRoot

Answer 1

To find the distance between the points (4, 9) and (1, 3), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \((x_1, y_1) = (4, 9)\) and \((x_2, y_2) = (1, 3)\).

Now we can plug in the values:

\[
d = \sqrt{(1 - 4)^2 + (3 - 9)^2}
\]
\[
= \sqrt{(-3)^2 + (-6)^2}
\]
\[
= \sqrt{9 + 36}
\]
\[
= \sqrt{45}
\]

Now, \(\sqrt{45}\) can be simplified:

\[
\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}
\]

However, since we need to select from the given options and none explicitly list \(3\sqrt{5}\), we focus on \(\sqrt{45}\), which matches option D.

Therefore, the distance between the points \((4, 9)\) and \((1, 3)\) is:

\[
\text{Answer: D. } \sqrt{45}
\]