Question

question 3 of 25
what is the distance between the points (21, -30) and (3, 8)? if necessary,
round your answer to two decimal places.

a. 56 units

b. 38 units

c. 33.47 units

d. 42.05 units

Explanation:

Answer:

D. 42.05 units

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

For the points \((21, -30)\) and \((3, 8)\):

• \(x_1 = 21\), \(y_1 = -30\)
• \(x_2 = 3\), \(y_2 = 8\)

First, calculate the differences:
\(x_2 - x_1 = 3 - 21 = -18\)
\(y_2 - y_1 = 8 - (-30) = 38\)

Then, square these differences:
\((-18)^2 = 324\)
\(38^2 = 1444\)

Add the squared differences:
\(324 + 1444 = 1768\)

Take the square root:
\(d = \sqrt{1768} \approx 42.05\) (rounded to two decimal places).