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The length of a line segment is of 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.

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Let two ordinate of the other end R be Y Coordinates of other end R are (10,y) i.e., R(10,y)

Distance PR=10   [given]

Squaring both sides

⇒ 100=73+y2+6y

⇒ y2+6y+73-100=0

⇒ y2+6y-27=0

Splitting the middle term

⇒ y2+9y-3y-27=0

⇒ y(y+9)-3(y+9)=0

⇒ (y+9)(y-3)=0

⇒ y= -9, y=3

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