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 coordinate of a?

Answer 1

GIVEN

Let the point be A

The abscissa of A point = its ordinate

Distance from Point B(1,3) is 10units.

TO FIND

Coordinates of A

SOLUTION

We know that,

Distance^2 = (x2 - x1)^2 + (y2 - y1)^2

Here it is given that,

x2 = 1 and y2 = 3

x1 = y1 = z

Lets subsitute the value to get our answer :-

10^2 = (1 - z)^2 + (3 - z)^2

=> 100 = 1 + z^2 - 2z + 9 + z^2 - 6z

=> 100 = 10 + 2z^2 - 8z

=> 0 = - 90 + 2z^2 - 8z

=> 2z^2 - 8z - 90 = 0

=> z^2 - 4z - 45 = 0

=>z^2 - 9z + 5z - 45 = 0

=> z(z - 9) + 5(z - 9) = 0

=> (z - 9) (z +5) = 0

=> z = 9 or z = -5

Hence the coordiantes of A are (9,9) [ANS]

Answer 2

Step-by-step explanation:

GIVEN

Let the point be A

The abscissa of A point = its ordinate

Distance from Point B(1,3) is 10units.

TO FIND

Coordinates of A

SOLUTION

We know that,

Distance^2 = (x2 - x1)^2 + (y2 - y1)^2

Here it is given that,

x2 = 1 and y2 = 3

x1 = y1 = z

Lets subsitute the value to get our answer :-

10^2 = (1 - z)^2 + (3 - z)^2

=> 100 = 1 + z^2 - 2z + 9 + z^2 - 6z

=> 100 = 10 + 2z^2 - 8z

=> 0 = - 90 + 2z^2 - 8z

=> 2z^2 - 8z - 90 = 0

=> z^2 - 4z - 45 = 0

=>z^2 - 9z + 5z - 45 = 0

=> z(z - 9) + 5(z - 9) = 0

=> (z - 9) (z +5) = 0

=> z = 9 or z = -5

Hence the coordiantes of A are (9,9) [ANS]

hope this helps you!!