Question

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 cordinates of A

Answer 1

Let abscissa = ordinate = x
Then, point A is (x,x).
Given, AB = 10
$\sqrt{ {(x - 1)}^{2} + {(x - 3)}^{2} } = 10 \\ {(x - 1)}^{2} + {(x - 3)}^{2} = 100 \\ ( {x}^{2} - 2x + 1) + ( {x}^{2} - 6x + 9) = 100 \\ {x}^{2} - 4x - 45 = 0 \\ (x - 9)(x + 5) = 0 \\ x = 9 \: \: or \: \: - 5$
Thus, A is (9,9) or (-5,-5)

Answer 2

$\huge\bf{Answer:-}$

Refer the attachment.