Question

prove that A(2,1) B(0,3) and C(-2,1) are the three vertices of an isosceles right angled triangle .Hence find the coordinate of point D,if ABCD is a square. ​

Answer 1

Answer:

D =(0,1)

Step-by-step explanation:

use distance formula i.e., √{(x2-x1)^2+(y2-y1)^2}

AB =√{(0-2)^2 + (3-1)^2} = √{(-2)^2 + (2)^2} = √8

BC = √{(-2-0)^2 + (1-3)^2} = √{(-2)^2 + (2)^2} = √8

AC =√{(-2-2)^2 + (1-1)^2} = √(-4)^2 = 4

therefore AB=BC i.e., triangle ABC is an isosceles triangle

PYTHAGORAS THEOREM

AB^2 + BC^2 = CA^2

AB^2 + BC^2 = (√8)^2 + (√8)^2   =  16

CA^2 = (4)^2 =  16

therefore triangle ABC is an isosceles right angle triangle

AC is the midpoint of BD

midpoint formula = ({x1+x2}/2 , {y1+y2}/2)

D = ({2-2}/2 , {1+1}/2)

D = (0,1)

Answer 2

Answer:

hope it helps

Step-by-step explanation:

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