Question

points a, b, and c are collinear. point b is between a and c. solve for x.

1. find x if ab = x + 14, ac = 23 and bc = x + 13. x =
2. ac = x + 19, ab = 7, and bc = 2x + 19. find x. x =
3. find x if ab = 2x - 1, bc = 11, and ac = 5x - 2. x =
4. bc = 9, ab = x - 2, and ac = -2 + 4x. find x. x =

points a, b, and c are collinear. point b is between a and c. find the length indicated.

1. ac = 1 + 4x, bc = 5x - 1, and ab = 2. find ac. ac =
2. find ab if bc = 11, ac = 5x - 3, and ab = x - 2. ab =
3. find ab if bc = 2x + 28, ac = 10, and ab = 2x + 22. ab =
4. find bc if ac = 14, bc = x + 10, and ab = x + 10. bc =

find the distance between each pair of points. simplify the radical if possible.
21)
image of coordinate grid with points
d =
22)
image of coordinate grid with points
d =

1. (-4, 6), (-2, 5) d =
2. (-1, 0), (5, 1) d =
3. (4, 1), (-2, -7) d =

Explanation:

Let's solve problem 23: Find the distance between the points \((-4, 6)\) and \((-2, 5)\).

Step 1: Recall the distance formula

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Step 2: Identify the coordinates

For the points \((-4, 6)\) and \((-2, 5)\), we have:
\(x_1 = -4\), \(y_1 = 6\)
\(x_2 = -2\), \(y_2 = 5\)

Step 3: Substitute the coordinates into the formula

First, calculate the differences in the \(x\)-coordinates and \(y\)-coordinates:
\(x_2 - x_1 = -2 - (-4) = -2 + 4 = 2\)
\(y_2 - y_1 = 5 - 6 = -1\)

Then, square these differences:
\((x_2 - x_1)^2 = (2)^2 = 4\)
\((y_2 - y_1)^2 = (-1)^2 = 1\)

Next, add these squared differences:
\(4 + 1 = 5\)

Finally, take the square root of the sum:
\[
d = \sqrt{5}
\]

Answer:

\(\sqrt{5}\)