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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1 Answer
Alan P.
Apr 25, 2015

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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