Question

if a (-2,1) , b(9,0) , c(4,b) and d (1,a) are vertices of a parallelogram ,abcd . find the values of a and b and hence find the length of each side

Answer 1

To solve this question, we need to understand the properties of a parallelogram.

PROPERTIES

1) Opposite sides are parallel and equal.

2) Opposite angles are equal.

The property number 1 is the most vital in this question.

In this question we will also use the following facts to solve for the unknowns.

A) Parallel lines have equal gradients.

B) Gradient of a line equals change in y divide by change in x.

C) The length of a line given its coordinates is given by:

L = √{(y - y)² + (x - x) ²}

In this case :

Line AB is parallel to line DC and line AD is parallel to line BC.

The symbol that denotes parallel lines is : //

Meaning :

AB // DC and AD // BC

Also : AB = DC and AD = BC

With the concept above we will be able to get the values of a and b and also the lengths of the sides of the parallelogram.

Find attached the step by step calculations.

Answer 2

Answer:

√1297

_________; ( 13/3 , 4)

2