Question

find the distance d(a,b) between points a and b. a(7, -7); b(7,4) d(a,b)=□ (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall distance formula

For points \( A(x_1,y_1) \) and \( B(x_2,y_2) \), distance \( d(A,B)=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Here, \( x_1 = 7,y_1=-7,x_2 = 7,y_2 = 4 \).

Step2: Substitute values

\( x_2 - x_1=7 - 7 = 0 \), \( y_2 - y_1=4-(-7)=4 + 7 = 11 \).

Step3: Calculate distance

\( d(A,B)=\sqrt{0^2+11^2}=\sqrt{121}=11 \).

Answer:

11