Given: two opposites vertices of square are (1,2) and (5,8)
To find: opposite’s vertices of a square and equation of sides.
Let A (1, 2) be the vertex of square ABCD and BD be the diagonal that is along the line 8x − 15y = 0
Equation of the given line is, 8x – 15y = 0
⇒ - 15y = - 8x
Comparing this equation with y = mx + c
We get, m
So, the slope of BD will be .
Here, we have to find the equations of sides AB and AD.
We know that the equations of two lines passing through a point x1,y1 and making an angle α with the line whose slope is m.
m, x1 = 1, y1 = 2, α = 45∘
So, the equations of the required sides are
⇒ 23x – 7y – 9 = 0 and 7x + 23y – 53 = 0
Hence, equation of sides is 23x – 7y – 9 = 0 and 7x + 23y – 53 = 0
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