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NeTakaya
2 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]2 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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Step-by-step explanation:

Each of the given table data of in the tables are analysed to find direct variation;

Table 1

x,               -3,                 -1,                 2,                5,                10

y,              -4.5,              -3.0,             -1.5,             0.0,              1.5              

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Table 2      

x,             -5.5,               -4.5,            -3.5,            -2.5,             -1.5

y,              10,                   8,                 6,              4,                  2

10/(-5.5) = -20/11  ≠ 8/(-4.5) = -16/9

However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2

Adjusted direct variation

Table 3              

x,              -5.5,               -5.5,             -5.5,           -5.5,            -5.5

y,              -3,                    -1,                 2,                5 ,              10                  

-3/(-5.5) ≠ -1/-5.5

No direct variation

Table 4

x,              -3,                    -1,                2,                  5,             10

y,              -7.5,                 -2.5,            5.0 ,              12.5,         25  

 -7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10

Direct variation exists        

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