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Distance between two points AYD
Find the distance between the points (1, 4) and (-10, -3).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
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Verified Answer :

GinnyAnswer

To find the distance between two points \(\((x_1, y_1)\)\) and \(\((x_2, y_2)\)\) on the Cartesian plane, we use the distance formula:

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

Let's use the coordinates of the two points given:
\(\[ (x_1, y_1) = (1, 4) \]\)
\(\[ (x_2, y_2) = (-10, -3) \]\)

First, we find the differences in the x-coordinates and y-coordinates:
\(\[ x_2 - x_1 = -10 - 1 = -11 \]\)
\(\[ y_2 - y_1 = -3 - 4 = -7 \]\)

Next, we square these differences:
\(\[ (-11)^2 = 121 \]\)
\(\[ (-7)^2 = 49 \]\)

We then add these squared values together:
\(\[ 121 + 49 = 170 \]\)

Finally, we take the square root of this sum to find the distance:
\(\[ d = \sqrt{170} \]\)

Therefore, the distance between the points \(\((1, 4)\)\) and \(\((-10, -3)\)\) can be expressed as a simplified radical:
\(\[ \boxed{\sqrt{170}} \]\)