Answer:
Explanation:
To find the lengths, we use the Pythagorean theorem, which states (a^2)+(b^2)=(c^2) where c^2 is the hypotenuse, length opposite of the right angle. For the first set of coordinates J and K, we find the horizontal and vertical differences between them to represent sides a and b. Which would be a horizontal length of 8 and a vertical length of 3.
(8^2)+(3^2)=c^2
73=c^2
c=square root of 73
(I've added a picture of a graph I drew below)
I would suggest you draw graphs of the points and use the Pythagorean theorem to conceptualize it, but I'll list the rest of the measurements below.
MN:
Vertical length between 2 and -3 = 5
Horizontal length between 7 and 1 = 6
(6^2)+(5^2)=c^2
36+25=c^2
61=c^2
c= square root of 61
PQ:
Vertical length between -6 and -2 = 4
Horizontal length between -8 and -3 = 5
(5^2)+(4^2)=c^2
25+16=c^2
41=c^2
c= square root of 41
As for the "checking all the statements" part, none of them are true because none of the lengths are equal.
Hope this helps! (Sorry for being so late)