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Rect. HIJKpoints are H (-4,1), I (1,1) J(1,-2) & K(-4,-2). LMNO points are L(-1,3),...

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connorcolin3 | (Level 1) Valedictorian

Posted December 19, 2011 at 8:16 AM via web

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Rect. HIJKpoints are H (-4,1), I (1,1) J(1,-2) & K(-4,-2). LMNO points are L(-1,3), M(2,3), N (2,-3) & O(-1,-3). How can I make them congruent

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted December 19, 2011 at 10:25 AM (Answer #1)

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First we will find the length of the lines of each rectangle.

==> HIJK.

`l HI l = sqrt((1+4)^2 + (1-1)^2)= 5`

`l IJ l = sqrt((1-1)^2 + (1+2)^2)= 3`

`l JK l = sqrt((1+4)^2 + (2-2)^2) = 5`

`l KH l = sqrt((-4+4)^2 + (-2-1)^2)= 3`

`` ==> LMNO

`l LM l = sqrt((-1-2)^2 + (3-3)^2)= 3`

`l MN l = sqrt((2-2)^2 + (3-(-3))^2) = 6`

`l NOl = sqrt((2+1)^2+ (-3+3)^2)= 3`

`l OL l = sqrt((-1+1)^2 + (-3-3)^2)= 6`

 

In order to make both rectangles congruent, we need to make the sides MN and OL  5 instead of 6 .

To do that we might consider moving the points one unit further .

One example could be Moving point N one unit up from (2,-3) to be (2,-2), and the point O from (-1, -3) to be (-1, -2) .

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