Question

1. Reasons quantitatively. AB lies on the number line. The coordinate of point A is -6. Given thay AB = 20, what are two possible coordinates for point B?2. Given: Point K is between points H and J, HK = x - 5, KJ = 5x - 12, and HJ = 25. Find the value of x.

Answer 1

The distance in a coordinate line is given by:

`d(A,B)=\lvert B-A\rvert`

in this case we know that A=-6 and we would like to know the value of B so that the distance is 20. Plugging this values in the equation we have:

`\begin{gathered} \lvert B-(-6)\rvert=20 \\ \lvert B+6\rvert=20 \end{gathered}`

Now we need to remember the property:

`\begin{gathered} \lvert x\rvert=a \\ \text{implies} \\ x=\pm a \end{gathered}`

Using this we have:

`\begin{gathered} \lvert B+6\rvert=20 \\ B+6=\pm20 \\ B=-6\pm20 \end{gathered}`

Then:

`\begin{gathered} B=-6+20=14 \\ B=-6-20=-26 \end{gathered}`

Therefore the two possible coordinates for B are 14 and -26.