Evalualecos65tan 75° tan I0° tan 40 lall JU lShow thai the points A(

1.	Evalualecos65tan 75° tan I0° tan 40 lall JU lShow thai the points A(2,-2), B(14, 10), C(11, 13) and D(-1,1) are the vertices of a rectanglenn ilnd 0010. y) 1s 10 units.OR
Answer» For a rectangle, CASE 1 AB=CD (2-14)^2+ (-2-10)^2= (11+1)^2+ (13-1)^2 288 = 288 case 1 verified CASE 2 AD=BC (2+1)^2+ (-2-1)^2= (14-11)^2+ (10-13)^2 18=18 case 2 verified CASE 3 AC=BD (2-11)^2+ (-2-13)^2= (14+1)^2+ (10-1)^2 306=306 case 3 verified Therefore it is a rectangle.

Evalualecos65tan 75° tan I0° tan 40 lall JU lShow thai the points A(2,-2), B(14, 10), C(11, 13) and D(-1,1) are the vertices of a rectanglenn ilnd 0010. y) 1s 10 units.OR

Answer»

For a rectangle,

CASE 1 AB=CD

(2-14)^2+ (-2-10)^2= (11+1)^2+ (13-1)^2

288 = 288

case 1 verified

CASE 2 AD=BC

(2+1)^2+ (-2-1)^2= (14-11)^2+ (10-13)^2

18=18

case 2 verified

CASE 3 AC=BD

(2-11)^2+ (-2-13)^2= (14+1)^2+ (10-1)^2

306=306

case 3 verified

Therefore it is a rectangle.