On a coordinate grid, JK has endpoint J at (15, −2), the midpoint of is M (1, −7). What is the length of JK?

1 Answer
Apr 25, 2015

Step 1: Determine the coordinates of the endpoint K
Step 2: Use Pythagorean Theorem to determine the length $| J K |$

Step 1
If M is the mid point of JK then the changes in $x$ and $y$ are the same from J to M and from M to K
$\Delta x \left(J : M\right) = 1 - 15 = - 14$
$\Delta y \left(J : M\right) = - 7 - \left(- 2\right) = - 5$

The coordinates of K are
$M + \left(- 14 , - 5\right) = \left(1 , - 7\right) + \left(- 14 , - 5\right) = \left(- 13 , - 12\right)$

Step 2:
$| J K | = \sqrt{{\left(\Delta x \left(J : K\right)\right)}^{+} {\left(\Delta y \left(J : K\right)\right)}^{2}}$
based on the Pythagorean Theorem

$| J K | = \sqrt{{\left(- 13 - 15\right)}^{2} + {\left(- 12 - \left(- 2\right)\right)}^{2}}$

$= \sqrt{884}$

$= 2 \sqrt{441}$