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NeTakaya
3 years ago
15

Help please? if JKhas endpoints J(-2,3) and k(6,5), and LN has endpoints L(0,7) and N(4,1), then JK and LN have the same midpoin

t. If GH has endpoints G(-8,1) and H(4,5), then the midpoint M of GH lies on the line y= -x+1.
Mathematics
1 answer:
Furkat [3]3 years ago
7 0
In this item, it is assumed that what is asked is that if the statement is TRUE or FALSE. 

Part A:
The coordinates of the midpoint of the given endpoints of the line is equal to half of the sum of the coordinates.

Line JK
           abscissa = (-2 + 6) / 2 = 2
           ordinate = (3 + 5) / 2 = 4
Midpoint is (2, 4)

Line LN
           abscissa = (0 + 4) / 2 = 2
           ordinate = (7 + 1) / 2 = 4
Midpoint is (2, 4)

Hence, the statement is TRUE.

Part B:
              abscissa = (-8 + 4)/ 2= -2
             ordinate = (1 + 5) / 2 = 3

Midpoint  = (-2, 3)

Substituting the point to the given equation,
                  y = - x + 1
                  3 = -(-2) + 1 = 3

Thus, all statement is TRUE.
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We have been given in a cohort of 35 graduating students, there are three different prizes to be awarded. We are asked that in how many different ways could the prizes be awarded, if no student can receive more than one prize.

To solve this problem we will use permutations.

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We know that formula for permutations is given as

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On substituting the given values in the formula we get,

{_{3}^{35}\textrm{P}}=\frac{35!}{(35-3)!}=\frac{35!}{32!}

=\frac{35\cdot 34\cdot 33\cdot 32!}{32!}\\
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=35\cdot 34\cdot 33=39270

Therefore, there are 39270 ways in which prizes can be awarded.


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