Question

the abscissa of a point A is equal to its ordinate,and its distance fro the point B(1,3) is 10 units, what are the co ordinates of A

Answer 1

hey there here is your answer

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)

hope it helps...☺️

Answer 2

$\huge\bf{Answer:-}$

Refer the attachment.