Question

The length of a line segment is 10 units and the coordinates of one end point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.

Answer 1

Hint: Here we will consider the other coordinate as a variable ‘y’ and using the formula of distance between the two points the value can be calculated.

Complete step-by-step answer:

So here we are given a line segment AB of 10 units, at one end the coordinates are A (2,-3) and at the other end the coordinates are B (10, y).
Now as we know that the distance between two points is given by:
$d = \sqrt {{{({x_2} - {x_1})}^2} + {{({y_2} - {y_1})}^2}} \to (1)$.
Since we already know the distance between the coordinates is 10 units. We also know coordinates of point A and abscissa of point B we have to find the ordinate putting the values that we know in the equation (1) we get
$10 = \sqrt {{{(10 - 2)}^2} + {{(y - ( - 3))}^2}} $
Now squaring on both sides we get
$
  100 = 64 + {(y + 3)^2} \\
   \Rightarrow {(y + 3)^2} = 36 \\
   \Rightarrow y + 3 = \pm 6 \\
   \Rightarrow y = - 9,3 \\
$
Ordinates of the line segments are $y = - 9,3$.

Note: In these kinds of questions as you are given the distance between coordinates apply the distance formula and put the value of knowns to get the values of unknown.