Question

The length of a line segment is 10 units. If one end is (2, –3) and the abscissa of the other end is 10, then its ordinate is either 3 or –9. Give justification for the two answers.

NCERT Class X
Mathematics - Exemplar Problems

Chapter _QUESTION PAPER SET 12

Answer 1

Let ordinatre of the point be y

So,
$\sqrt{ (2-10)^{2} + (-3-y)^{2} } = 10$
or, 64 + (y+3)(y+3) = 100
or, (y+3)(y+3) = 36
or, y+3 = 6,-6
or, y = 6-3, -6-3 = 3,-9 (proved)

Answer 2

Given line segment AB = 10units

A (2, -3) and B (10, y)

AB = 102102 =(10−2)2+(y+3)2−−−−−−−−−−−−−−−−√(10−2)2+(y+3)2

⟹100=64+y2+6y+9⟹100=64+y2+6y+9

⟹y2+6y−27=0⟹y2+6y−27=0

⟹(y−3)(y+9)=0⟹(y−3)(y+9)=0

∴∴ y =3 or y = -9