Question

If the points A(–2, –1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram, taken in order, find the value of a and b.

Answer 1

AB = CD...... Equation 1

(opp sides of parallelogram)

Find the length of AB through distance formula

A = (-2,-1) = (x1, y1)

B = (a, 0) = (x2, y2)

Distance formula = rt [(0-(-1))^2 + (a-(-2))^2 ]

Hope you know that formula rt [(y2-y1) ^2 + (x2-x1) ^2]

Rt (1+(a+2)^2)

Rt (1+ a^2 + 4a + 4)

Rt (a^2 + 4a + 5) units

Similarly we will find the value of CD through distance formula

and then equate it in the equation 1

You will get your answer!

Hope it helps!

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