Q. 135.0( 1 Vote )

# If two opposites vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.

Given: two opposites vertices of square are (1,2) and (5,8)

To find: opposite’s vertices of a square and equation of sides.

Explanation:

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. Here,

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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