*. If (2,3) and (-6,5) are the end points of diagonal of a square. Find the equation of another diagonal. Please help with this question..

 y = 4x + 12    (edited to reflect a SQUARE)

Step-by-step explanation:

Opposite Diagonal of a square means the line goes through the midpoint and has the opposite reciprocal slope.

Use the Midpoint formula:    

Use the Slope formula:  

Opposite Diagonal slope is opposite (change the sign) and reciprocal (flip the fraction)  → m⊥ = + 4

Now use the Point-Slope formula:   y - y₁ = m⊥(x - x₁)    where

y - 4 = 4(x + 2)

y - 4 = 4x + 8

   y = 4x + 12

Simple question

slope of on le diagonal,whose coordinates are given=

now we know that diagonals of square are perpendicular to each other

and we also know that if there are two perpendicular lines have slope m1 and m2 respectively,then

so if one diagonal's slope is -1/4 then other diagonal's slope will be 4

now we know that all the equation of a line is in the form

y=mx+c

where m is slope

so simply put the value of m=4

y=4x+c...i)

we also know that the line of equationi) will pass through the midpoint coordinates of first diagonal

mid point of first diagonal ={(2-6)/2 ,(5+3)/2}=(-2,4)

put this value of x and y in i) equation

4=-8+c

c=12

hence putting the value of c in equation I) we get the equation of line as

y=4x+12

y-4x-12=0