Question

find the distance d(a, b) between points a and b. a(4, -2); b(4,2) d(a,b)=□ (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall distance formula

For two points \((x_1,y_1)\) and \((x_2,y_2)\), distance \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(A(4,-2)\), so \(x_1 = 4,y_1=-2\); \(B(4,2)\), so \(x_2 = 4,y_2 = 2\).

Step2: Substitute values into formula

Substitute \(x_1 = 4,y_1=-2,x_2 = 4,y_2 = 2\) into the formula:
\(d(A,B)=\sqrt{(4 - 4)^2+(2 - (-2))^2}\)

Step3: Simplify the expression

First, calculate inside the square root: \((4 - 4)^2=0^2 = 0\), \((2 - (-2))^2=(2 + 2)^2=4^2 = 16\). Then \(d(A,B)=\sqrt{0 + 16}=\sqrt{16}=4\).

Answer:

\(4\)