Question

Find the coordinates of the points which divide the line segment joining the points $(-4,0)$ and $(0,6)$ in four equals parts.

• A. $(-3,\frac{3}{2}),(-2,3),(-1,\frac{9}{2})$
• B. $(-3,\frac{1}{2}),(-1,3),(-1,\frac{9}{2})$
• C. $(-2,1),(-1,3),(-1,\frac{1}{2})$
• D. $(-1,2),(-2,3),(-1,\frac{1}{2})$

Answer 1

The correct option is A $(-3,\frac{3}{2}),(-2,3),(-1,\frac{9}{2})$

Given points are A(-4, 0) and B(0, 6)
Mid-point of A and B will be (x, y), then $x=\frac{-4+0}{2}=-2$
and $y=\frac{0+6}{2}=3$, therefore mid-point is (-2, 3).
Now mid-point of (-4, 0) and (-2. 3) will be
$x_1=\frac{-4-2}{2}=-3$ and $y_1=\frac{0+3}{2}=\frac{3}{2}i.e.,(-3,\frac{3}{2})$
Again mid-point of (-2, 3) and (0, 6) will be
$x_2=\frac{-2+0}{2}=-1and{y}_2=\frac{3+6}{2}=\frac{9}{2}i.e.,(-1,\frac{9}{2})$
Therefore three points are $(-3,\frac{3}{2}),(-2,3),(-1,\frac{9}{2})$