Consider the following number line: <------------------M------------------G------------------> 0 3 10 Find the location (or coordinate) of the point B if M is the midpoint of BG.
Answer (1)
To find the coordinate of point B on the number line, we start by understanding the given information. We know:
M is the midpoint of BG.
M is located at coordinate 3.
G is located at coordinate 10.
Since M is the midpoint of BG, it means M is exactly halfway between B and G. The formula to find the midpoint M of a segment between two points B (located at coordinate x 1 ) and G (located at coordinate x 2 ) is given by:
M = 2 x 1 + x 2
We know M = 3 and G = 10 , so we plug these values into the formula:
3 = 2 x 1 + 10
To solve for x 1 (which represents the coordinate of point B), we'll start by getting rid of the fraction. We can do this by multiplying both sides of the equation by 2:
6 = x 1 + 10
Next, subtract 10 from both sides to isolate x 1 :
6 − 10 = x 1
Simplifying that gives:
x 1 = − 4
Thus, the coordinate of point B is -4. This means that point B is located 4 units to the left of zero on the number line.
