Question

A segment has endpoints A (-1, 1) and B (8, 4) . If the segment is divided into four equal parts, the coordinates of the point closest to point A are _____. (7/2, 5/2) (5/4, 7/4) (23/4, 13/4)

Answer 1

Answer:

ANSWER IS ( 5/4 , 7/4 ).

Step-by-step explanation:

Answer 2

Line is divided into 4 equal parts.

we have to find a point which is closest to point A.

So that means required point P(x,y) is at 1 unit away from A(-1,1) and 3 unit away from B(8,4)

Now we just need to use section formula to get the coordinate of required point using m1=1 and m2=3

$\left ( \frac{m_1x_2+m_2x_1}{m_1+m_2} , \frac{m_1y_2+m_2y_1}{m_1+m_2} \right )$

$= \left ( \frac{1*8+3*(-1)}{1+3} , \frac{1*4+3*1}{1+3} \right )$

$= \left ( \frac{8-3}{4} , \frac{4+3}{4} \right )$

$= \left ( \frac{5}{4} , \frac{7}{4} \right )$

So the final answer is $\left ( \frac{5}{4} , \frac{7}{4} \right )$.