Question

1. graph the points in the coordinate plane : A (-2,1) B (2,1) C(3,2) and D (3,-2) . is AB congruent to CD ?2. the endpoints of CD are C (-1,6) and D (7,8) . find the coordinate of midpoint M . hint * use the midpoint and make sure you answer is written as a point* 3. find the distance between the 3 points: A (3,7) and B( 6,5) (all for question 1)

Answer 1

1) Graph the points: A(-2, 1), B(2, 1), C(3, 2), D(3, -2):

We can see that the segments AB and CD has the same lenght of 4 units, so they are congruents.

2) The midpoint M between C(-1, 6) and D(7, 8) is:

`\begin{gathered} M=(D-C)/(2) \\ M=((7-(-1))/(2),(8-6)/(2)) \\ M=((7+1)/(2),(2)/(2)) \\ M=(4,1) \end{gathered}`

The midpoint M is (4, 1).

3) The distance between A(3, 7) and B(6, 5) is:

`\begin{gathered} A=(x_1,y_1)=(3,7) \\ B=(x_2,y_2)=(6,5) \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(6-3)^2+(5-7)^2} \\ d=\sqrt[]{3^2+2^2} \\ d=\sqrt[]{9+4}=\sqrt[]{13} \end{gathered}`