Question

given a line ABCD in which ab = BC = CD B is (0, 3 )and C is( 1, 8 )find the coordinates of a and d

Answer 1

Answer:

A = (-1 , -2)

D = (2 , 13)

Step-by-step explanation:

AB = BC = CD

B = (0 , 3)   C = ( 1 , 8)

BC = √(1 - 0)² + (8-3)² = √26

Slope = (8-3)/(1 - 0) = 5

y = 5x + c

3 = 0 + c

=> c = 3

y = 5x + 3

(Ax , Ay)

AB = √(Ax - 0)² + (Ay - 3)²  = BC

=> √(Ax - 0)² + (Ay - 3)²  = √26

=> Ax² + (Ay -3)² = 26

=> Ax² + (5Ax + 3 - 3)² = 26

=> Ax² + 25Ax² = 26

=> 26Ax² = 26

=> Ax² = 1

=> Ax = ±1

Ax = 1 is C

=> Ax = -1

Ay = -2

A = (-1 , -2)

Simialrly

Dx , Dy

(Dx - 1)² + (Dy - 8)² = 26

=> (Dx - 1)² + (5Dx - 5)² = 26

=> (Dx - 1)² = 1

=> Dx - 1 = ±1

=> Dx = 2 , 0  

0 is B

=> Dx = 2

Dy = 13

D = (2 , 13)