Question

The abscissa of a point A Is equal to its ordinate and its distance from the point B(1,3) is 10 units .what are the coordinates of A

Answer 1

"Given

abscissa = ordinate

let x = y = k. then A (x,y) = (k,k)

B (1,3)

condition is

distance of AB = 10

squaring on both sides

(AB)^2 = 100

{(k - 1)}^{2}  +  {(k - 3)}^{2}  = 100 \\  {k}^{2}  + 1 - 2k +  {k}^{2}  + 9 - 6k = 100 \\ 2 {k}^{2}  - 8k + 10 = 100 \\  {k}^{2} -  4k + 5 = 50 \\  {k}^{2}  - 4k - 45 = 0 \\  {k}^{2}   + 5k  - 9k - 45 = 0 \\  k(k + 5) - 9(k + 5) = 0 \\ (k + 5)(k - 9) = 0 \\ k =  - 5 \: or \: 9

therefore k = -5 or 9

so A(x,y) can be (-5,-5) or (9,9)"

Answer 2

$\huge\bf{Answer:-}$

Refer the attachment.