Question

the distance d between two points is given. Find the possible values of b. (0,b),(5,12); d= 13

Answer 1

dont use pictures to explain it

Answer 2

To find the possible values of \( b \) such that the distance \( d \) between the points \( (0,b) \) and \( (5,12) \) equals 13, we can use the distance formula:

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

Here, the points are \( (x_1, y_1) = (0, b) \) and \( (x_2, y_2) = (5, 12) \). Plugging these points into the distance formula gives:

\[
d = \sqrt{(5 - 0)^2 + (12 - b)^2}
\]

Substituting \( d = 13 \):

\[
\sqrt{5^2 + (12 - b)^2} = 13
\]

Squaring both sides to eliminate the square root results in:

\[
25 + (12 - b)^2 = 169
\]

Subtracting 25 from both sides:

\[
(12 - b)^2 = 144
\]

Next, we take the square root of both sides:

\[
12 - b = 12 \quad \text{or} \quad 12 - b = -12
\]

Solving the first equation \( 12 - b = 12 \):

\[
-b = 0 \implies b = 0
\]

Now solving the second equation \( 12 - b = -12 \):

\[
-b = -24 \implies b = 24
\]

Thus, the possible values for \( b \) are:

\[
\boxed{0 \text{ and } 24}
\]