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Determine if triangle XYZ with coordinates X(1, 1), Y(5, 6), and Z(6, 2) is a right triangle. Use evidence to support your claim.

User Simon M
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In order to find this out we need to find the slopes of all those lines in question. Line XY, line YZ, and line XZ. If any 2 of those slopes are opposite reciprocals of each other, then those 2 lines are perpendicular and where perpendicular lines meet, a right angle is formed and this would, in fact, be a right triangle. So we need the slope formula to get the job done. The slope between X and Y first:
m_(XY)=(6-1)/(5-1)=(5)/(4). The slope of line XY is 5/4. Now for the slope of line YZ:
m_(YZ)=(2-6)/(6-5)=(-4)/(1)=-4. Finally we find the slope of line XZ:
m_(XZ)=(2-1)/(6-1)=(1)/(5). None of the slopes are opposite reciprocals of each other so this is not a right triangle.

User Hugo Logmans
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