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

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

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Answer 1 · 2015-04-25T14:59:56

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

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
$Delta x(J:M) = 1-15 = -14$
$Delta y(J:M) = -7-(-2) = -5$

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

Step 2:
$| JK | = sqrt((Delta x(J:K))^ + (Delta y(J:K))^2)$
based on the Pythagorean Theorem

$|JK| = sqrt( (-13-15)^2 + (-12-(-2))^2)$

$=sqrt(884)$

$=2sqrt(441)$

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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

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