Question

14. Find the angle between the diagonals of a parallelogram whose vertions taken in order
are A(1,-2) ,b(2, 0) ,C(1, 6) and D(0,4)
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Answer 1

We can write the slope of diagonal AC.

m_1 = \dfrac{y_2-y_1}{x_2-x_1}m1=x2−x1y2−y1

m_1 = \dfrac{6-2}{1-1}m1=1−16−2

m_1 = \inftym1=∞

Similarly, We can write the slope of diagonal BD.

m_2 = \dfrac{y_2-y_1}{x_2-x_1}m2=x2−x1y2−y1

m_2 = \dfrac{4-0}{0-2}m2=0−24−0

m_2 = -2m2=−2

Let the angle between both the diagonals be \theta.

tan \theta = | \dfrac{m_1-m_2}{1+m_1m_2} |tanθ=∣1+m1m2m1−m2∣

|tanθ=1/2.

This is the required angle between both the diagonals.