Question

QR has the endpoints Q(–10, 7) and R(1, –4). Gabrielle found the x-coordinate of the point that partitions the directed line segment QR in the ratio 2:3. Her work is shown below. 1. X = (x2 – x1) + x1 2. =(1 – (–10)) + (–10) 3. =(11) – 10 4. = = The x-coordinate of the point P that partitions the directed line segment QR in the ratio 2:3 is , or –5.6. The y-coordinate of the point P is

Answer 1

The y- coordinate of point P is 2.6

Answer 2

Answer:

The x-coordinate of point P = -5.6

The y-coordinate of point P = 2.6

P(-5.6,2.6)

Step-by-step explanation:

QR has the endpoints Q(–10, 7) and R(1, –4).

Line segment QR divides at point P in ratio 2:3.

Using section formula:

$(x,y)\rightarrow (\frac{mx_2+nx_1}{m+n},\frac{mx_2+nx_1}{m+n})$

where,

$P\rightarrow (x,y)$

$m:n\Rightarrow 2:3$

$x\rightarrow \dfrac{2\cdot 1+3(-10)}{2+3}$

$x\rightarrow \dfrac{-28}{5}$

$x\rightarrow -5.6$

$y\rightarrow \dfrac{2\cdot -4+3\cdot 7}{2+3}$

$y\rightarrow \dfrac{13}{5}$

$y\rightarrow 2.6$

Hence, The x-coordinate of point P = -5.6 and The y-coordinate of point P = 2.6