Question

explore the distance tool and then answer each question to determine the distance between points d and a.
recall that the distance formula is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} =$ distance.
use the distance formula to determine the distance between points d and a.
$(x_2 - x_1)^2 = \square$ enter the square of the horizontal distance.
$(y_2 - y_1)^2 = \square$ enter the square of the vertical distance.
$(x_2 - x_1)^2 + (y_2 - y_1)^2 = \square$ enter the sum of the squares of the horizontal and vertical distances.
$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \square$ enter the approximate square root of the sum.
the coordinate plane of the explore tool represents a city measured in square blocks. investigate how the explore tool works before answering any questions.

Explanation:

Step1: Find coordinates of points

Assume \(A=(2, - 4)\) and \(D=(10,-9)\). Let \((x_1,y_1)=(2,-4)\) and \((x_2,y_2)=(10,-9)\)

Step2: Calculate \((x_2 - x_1)^2\)

\(x_2 - x_1=10 - 2=8\), so \((x_2 - x_1)^2=8^2 = 64\)

Step3: Calculate \((y_2 - y_1)^2\)

\(y_2 - y_1=-9-(-4)=-9 + 4=-5\), so \((y_2 - y_1)^2=(-5)^2 = 25\)

Step4: Calculate \((x_2 - x_1)^2+(y_2 - y_1)^2\)

\((x_2 - x_1)^2+(y_2 - y_1)^2=64 + 25=89\)

Step5: Calculate \(\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

\(\sqrt{89}\approx9.43\)

Answer:

\((x_2 - x_1)^2 = 64\)
\((y_2 - y_1)^2 = 25\)
\((x_2 - x_1)^2+(y_2 - y_1)^2 = 89\)
\(\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\approx9.43\)