Q26 of 77 Page 7


A line is of length 10 and one end is at the point (-3, 2). If the ordinate of theother end be 10, prove that the abscissa will be 3 or –9.


SOLUTION:

The two points are (-3, 2) and (x, 10). Their length is 10.

⇒ (3+x) 2 + 64 =10
⇒ x 2 + 6x + 9 + 64 = 100
⇒ x 2 + 6x – 27 = 0

⇒ x 2 + 9x – 3x – 27 = 0
⇒ x(x + 9) – 3(x + 9) = 0
⇒ (x – 3)(x + 9) = 0
⇒ x = 3 or –9.
Therefore the required abscissa will be 3 or –9.

More from this chapter

All 77 →
24
If the points (-1, 3), (1, -1) and (5, 1) are vertices of a triangle, find thelength of the median through third vertex.
 25
Find the lengths of the sides of the triangle whose vertices are A(3, 4), B(2,-1) and C(4, -6).
 27
Show that the points (-2, 6), (5, 3), (-1, -11) and (-8, -8) are the verticesof a rectangle.
 28
If a point (x, y) is equidistant from (6, -1) and (2, 3), find the relationbetween x and y.