Question

find the distance between points a and b.

Explanation:

Step1: Determine coordinates of points

Point \( A(6,-5) \), Point \( B(-7,7) \).

Step2: Use distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \)

Let \( (x_1,y_1)=(6,-5) \), \( (x_2,y_2)=(-7,7) \).
\( x_2 - x_1=-7 - 6=-13 \), \( y_2 - y_1=7-(-5)=12 \).

Step3: Calculate \( (x_2 - x_1)^2+(y_2 - y_1)^2 \)

\((-13)^2+12^2 = 169 + 144=313\).

Step4: Find the square - root

\( d=\sqrt{313}\approx17.7 \).

Answer:

\(17.7\) units