a line is of length 5 and one end is at point (1,-2); if the abscissa of the other end - Maths - Coordinate Geometry

Question

​a line is of length 5 and one end is at point (1,-2); if the
abscissa of the other end is 4, prove that its ordinate must be 2
or -6

Varun.Rawat · Accepted Answer

Let A1, -2 and B4, y be the given points
Now, AB = 5 units⇒4-12 + y+22 = 5      Distance between 2 points x1,y1 and x2,y2  = x2 - x12 + y2 - y12⇒4-12 + y+22 = 25⇒9 + y2 + 4 + 4y = 25⇒y2 + 4y - 12 = 0⇒y2 + 6y - 2y - 12 = 0⇒yy + 6 - 2y + 6=0⇒y - 2y + 6 = 0⇒y - 2 = 0   or  y+6 = 0⇒y = 2  or  y = -6

​a line is of length 5 and one end is at point (1,-2); if the abscissa of the other end is 4, prove that its ordinate must be 2 or -6.

a line is of length 5 and one end is at point (1,-2); if the abscissa of the other end is 4, prove that its ordinate must be 2 or -6.