Question

Find the value of k if the Triangle formed by A(9,-10),B(7,-3),C(0,k) right angle at B​

Answer 1

Step-by-step explanation:

area of triangle

= ½[ X1(Y2-Y3) + X2(Y3-Y1) + X3(Y1-Y2) ]

(X1, Y1) = (9,-10). (X2, Y2) = (7,-3) (X3,Y3) = 0,K

DISTANCE FORMULA = √(X2-X1)²+(Y2-Y1)²

AB² = (7-9)²+(-3+10)² = 4+49 =53

BC² = (0-7)²+(K+3)² = 49 + K²+9-6K = K²-6K+58

AC² = (0-9)²+(K+10)² = 81+K²+100+20K = K²+20K+181

AB²+BC²=AC² (PYTHAGORAS THEOREM)

53 + K²-6K+58 = K²+20K+181

26K = 181-111

26k = 70

k= 70/26

k= 35/13

putting value of k as 35/13 =y3

area of triangle =

½[ 9(-3-35/13) + 7(35/13+10) + 0(-10+3) ]

½ [ 9.-74/13 + 7.165/13 +0]

½[ 666/13 + 1155/13]

½ [1821/13]

= 1821/26 = 70.03846153846

I hope this is the answer but I am not sure

but if the answer is correct pls. mark me as brianliest