Question

find all the points having an x coordinate of 9 whose distance from the point (4,2) is 13

Answer 1

may this help u.....

Answer 2

Let the required point be ( x₁ , y₁ ), in the question it is already given that co ordinate of x is 9, so let the required point be ( 9 , y₁ ) .

Now, assume other point( 4 , 2 ) be ( x₂ , y₂ ).

By Distance Formula : -

$Distance = \sqrt{y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}$

Given in the question, distance between ( x₁ , y₁ ) and ( x₂ , y₂ ) is 13.

$13 = \sqrt{(2-y_{1})^{2} + (4-9)^{2}}$

13² = ( 2 - y )² + ( - 5 )²

169 = ( 2 - y )² + 25

169 - 25 = ( 2 - y )²

144 = ( 2 - y )²

$\pm$ 12 = ( 2 - y )²

12 = 2 - y   or    - 12 = 2 - y

y = 2 - 12  or        y = 2 + 12

y = - 10     or       y = 14

Therefore, the point having x co ordinate of 9 and is situated at the distance of 13 units from ( 4 , 3 ) is ( 9 , - 10 ) or ( 9 , 14 ).