Question

question 1 - 7
a submarine travels in a straight line from p(-4, 3) to q(6,-7). the submarine pauses to collect data at a point that is 3/4 of the way from p to q. select the coordinate pair whose the submarine will pause.
(-1,-2)
(8.5 - 4.5)
(1,-3)
(2,-4)

Explanation:

Step1: Find the x - coordinate of the point

Use the section - formula for x - coordinate $x=\ x_1+(x_2 - x_1)\times t$, where $(x_1,y_1)=(-4,3)$, $(x_2,y_2)=(6,-7)$ and $t = \frac{3}{4}$.
$x=-4+(6 - (-4))\times\frac{3}{4}=-4+(6 + 4)\times\frac{3}{4}=-4 + 10\times\frac{3}{4}=-4+\frac{30}{4}=\frac{-16 + 30}{4}=\frac{14}{4}=\frac{7}{2}=3.5$

Step2: Find the y - coordinate of the point

Use the section - formula for y - coordinate $y=y_1+(y_2 - y_1)\times t$.
$y=3+(-7 - 3)\times\frac{3}{4}=3+(-10)\times\frac{3}{4}=3-\frac{30}{4}=\frac{12-30}{4}=-\frac{18}{4}=-\frac{9}{2}=- 4.5$

Answer:

(3.5,-4.5) (It seems there is a formatting issue with the provided options in the image, but the calculated point is (3.5,-4.5))