Question

Find each graph, find (a) AB to the nearest tenth and (b) the coordinates of the midpoint of AB.

Answer 1

Answer: AB≈10,8, C(-1;0,5).

Explanation:

4.

`(-2,-2)\ \ \ \ (8,-6)\ \ \ \ \overline {AB}=?\\`

Equation of a straight line

`\boxed {\overline {AB}=√((x_B+x_A)^2+(y_B-y_A)^2) }`

`x_A=-2\ \ \ \ x_B=8\ \ \ \ y_A=-2\ \ \ \ \ y_B=-6\\\\\overline{AB}=√((8-(-2))^2+(-6-(-2))^2) \\\\\overline{AB}=√((8+2)^2+(-6+2)^2) \\\\\overline{AB}=√(10^2+(-4)^2) \\\\\overline{AB}=√(100+16) \\\\\overline{AB}=√(116) \\\\\overline{AB}\approx10,8.`

5.

`(-2,-2)\ \ \ \ (0,3)\ \ \ \ the\ midpoint\ C\ of\ AB=?\\`

Line Midpoint Equation

`\boxed {C_x=(X_A+X_B)/(2) }}\ \ \ \boxed {C_y=(Y_A+Y_B)/(2) }`

`X_A=-2\ \ \ \ \ X_B=0\ \ \ \ \ Y_A==-2\ \ \ \ Y_B=3\\\\C_x=(-2+0)/(2) \\\\C_x=(-2)/(2) \\\\C_x=-1.\\\\C_y=(-2+3)/(2)\\\\C_y=(1)/(2)\\\\ C_y=0,5.\\\\Hence,\ \ \ \ C_(AB)(-1;0,5).`