Question

question 14 of 25
what is the distance between the points (23, -33) and (4, 9)? if necessary, round your answer to two decimal places.
a. 37.46 units
b. 46.10 units
c. 42 units
d. 61 units

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign values

Let $(x_1,y_1)=(23,-33)$ and $(x_2,y_2)=(4,9)$. Then $x_2 - x_1=4 - 23=-19$ and $y_2 - y_1=9-( - 33)=42$.

Step3: Calculate squares

$(x_2 - x_1)^2=(-19)^2 = 361$ and $(y_2 - y_1)^2=42^2 = 1764$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=361 + 1764=2125$.

Step5: Calculate the square - root

$d=\sqrt{2125}\approx46.0977$.

Step6: Round the result

Rounding 46.0977 to two decimal places gives 46.10.

Answer:

A. 37.46 units