Question

1. Given line segment RB and on it is point C, if RB = 45 and CB = 3x - 12 and RC = 2x + 9, what is the value of x?
2. Using the same problem and values above, what is the length of line segment RC?
3.Use the coordinate plane/graph for the third problem.
Find the distance between A and D. Round your answer to the nearest hundredth place. *

Answer 1

Answer:

Step-by-step explanation:

1). If a point C is lying on a line segment RB,

   Then RB = RC + CB

   Since, RB = 45, CB = 3x - 12 and RC = 2x + 9

   45 = (2x + 9) + (3x - 12)

   45 = (2x + 3x) - 3

   48 = 5x

   x = $\frac{48}{5}$

   x = 9.6

2). Since, RC = 2x + 9

    RC = 2(9.6) + 9

          = 19.2 + 9

          = 28.2 units

3). Distance between the two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula,

  d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

  Distance between the points A(2, -2) and D(-2, 2) will be,

 $AD=\sqrt{(2+2)^2+(-2-2)^2}$  

         = $\sqrt{16+16}$

         = $4\sqrt{2}$  

         = 5.657

         ≈ 5.66 units