Without Distance Formula, Show that the Points M(1,7), N(4,8), O(5,5), and P(2,4) Form a Square. - Mathematics

Without distance formula, show that the points M(1,7), N(4,8), O(5,5), and P(2,4) form a square.

Sum

Slope of OM = `(7 - 5)/(1 -5) = 2/(-4) = (-1)/2`

Slope of PN = `(8 -4)/(4 -2) = 4/2` = 2

Slope of OM x Slope of PM = `1/2 xx 2 = -1`

`therefore` OM and PN bisect each other at 90°. Hence, MNOP is a square.

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