Question

One of the diagonals of a square is the portion of the
line x/2 + y/3 = 2 intercepted between the axes. Then the
extremities of the other diagonal are
a. (5,5), (1, 1) b. (0,0), (4, 6)
c. (0,0), (-1,1) d. (5,5), (4,6)​

Answer 1

Given :  One of the diagonals of a square is the portion of the

line x/2 + y/3 = 2 intercepted between the axes.

To find : extremities of the other diagonal

Solution:

x/2 + y/3 = 2

=> 3x + 2y  = 12

=> 2y = -3x  + 12

=> y = -3x/2  + 6

Slope  = -3/2

x = 0  , y  = 6   ( 0 , 6)

y = 0    x  = 4    ( 4, 0)

Mid point = ( 0 + 4)/2 , ( 6 + 0)/2

= 2 , 3

Slope of other Diagonal   = 2/3

a. (5,5), (1, 1)  - Slope  =  1

b. (0,0), (4, 6) slope = 3/2

c. (0,0), (-1,1)   slope = -1

d. (5,5), (4,6)​  slope =  - 1

none point have slope of 2/3

hence none of these points can be extremities of the other diagonal

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