1. Parallelogram is defined by the coordinates (-2, -4), (6, -4), (11, 2), and (3, 2), respectively. Use the Pythagorean Theorem to find the length of the parallelogram’s diagonal .
= a1 units

Gh There are two diagonals and the given points haven’t been labelled, so I need to give two answers.

The base and top have a length of 6-(-2)=8 units, 11-3=8 units.

The top is shifted 3-(-2)=5 units to the right of the base. If we drop a perpendicular on to the base it intercepts the base at (3,-4) forming a right triangle (3,2), (3,-4), (6,-4) where (3,-4) is the right angle. The hypotenuse is a diagonal so its length is √(3²+6²)=√45.

That’s one diagonal. Now for the other. Drop a perpendicular from the top right vertex (11,2) on to the extended base at (11,-4). The right triangle has a base length of 11-(-2)=13 units and a height of 2-(-4)=6 units just like the other diagonal. So, again using Pythagoras’ Theorem, the length of this second diagonal is √(13²+6²)=√205.

So the diagonals have lengths √45=6.7082 approx and √205=14.3178 approx units.

Check your question and label the vertices so that you can tell whether it’s the red or blue diagonal implied in the question.

by Top Rated User (645k points)