The length of HJ is 3.5 cm
<h3>What is Congruency?</h3>
Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.
Given:
AB = 3.5 cm, BC = 2.4 cm, and AC = 4.2 cm
As, ΔABC ≅ ΔHJK
So,
AB = HJ
BC = JK
AC = HK
Thus, HJ= AB = 3.5 cm
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When you arrange the N points in sequence around the polygon (clockwise or counterclockwise), the area is half the magnitude of the sum of the determinants of the points taken pairwise. The N determinants will also include the one involving the last point and the first one.
For example, consider the vertices of a triangle: (1,1), (2,3), (3,-1). Its area can be computed as
(1/2)*|(1*3-1*2) +(2*-1-3*3) +(3*1-(-1)*1)|
= (1/2)*|1 -11 +4| = 3
So in matt's equation, he made a mistake in the a transision from line 2 to line 3
in line 2: -4(-2)2
in line 3: -4(4)
the mistake is that -2 times 2 is not equal +4 it is equal to -4
also from lines 5 to 6 he made a mistake in order of opperations (mulit division then addition and subtract)
line 5: -10+30/5
line 6: 20/5
so he first subtracted 10 then divided, he should have divided then subtracted
so the equation should have equaled
Karen used the correct (-) times (+) property and the order of operations
so Karen is correct and Matt is wrong.
I think the only answer is E