Question

In a parallelogram A(1,-2),B(2,3),C(a,2) and D(-4,3) are points find the value of 'a'.

Answer 1

Answer:

use distance formula

Step-by-step explanation:

find distance ab and equate with cd

as ab=cd opposite sides of parallelogram ate equal

Answer 2

Answer:

A(1,-2),B(2,3),C(a,2) and D(-4,3) are the given points.

Here;

AD=BC[opposite sides of a parallelogram]

$= > \sqrt{ {(1 + 4)}^{2} + {( - 2 - 3)}^{2} } = \sqrt{ {(2 - a)}^{2} + {(3 - 2)}^{2} } \\ = > 25 + 25 = 4 - 4a + {a}^{2} + 1 \\ = > 50 = 5 - 4a + {a}^{2} \\ = > {a}^{2} - 4a - 45 = 0 \\ = > {a}^{2} - 9a + 5a - 45 = 0 \\ = > a(a - 9) + 5(a - 9) = 0 \\ = > (a - 9)(a + 5) = 0 \\ therefore \: a = 9 \: or \: a = - 5$