Question

find the point P along the directed line segment from point A(-11,1) to point B(0,-3) that divides the segment in the ratio 3 to 4

Answer 1

Hi,

See the working out on the piece of paper and don’t hesitate to ask any questions if confused!!

Answer 2

Answer:

$\textsf{P}=\left(-\dfrac{44}{7},-\dfrac{5}{7}\right)$

Step-by-step explanation:

Given:

• A = (-11, 1)
• B = (0, -3)
• Ratio 3 : 4

Therefore, point P on the segment AB should be 3/7 of the way from point A.

$x_P=\dfrac{3}{7}(x_B-x_A)+x_A=\dfrac{3}{7}(0-(-11))-11=\dfrac{-44}{7}$

$y_P=\dfrac{3}{7}(y_B-y_A)+y_A=\dfrac{3}{7}(-3-1)+1=-\dfrac{5}{7}$

$\implies \textsf{P}=\left(-\dfrac{44}{7},-\dfrac{5}{7}\right)$

or P = (-6.3, -0.7) to 1 decimal place

(Please see attached image, where the segment AB has been divided into 7 equal parts.)