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

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 =
`(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 =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

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

`AD=√((2+2)^2+(-2-2)^2)`

=
`√(16+16)`

=
`4√(2)`

= 5.657

≈ 5.66 units