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 point where the submarine will pause
(-1,-2)
(3.5,-4.5)
(4,-5.5)
(5,-6)

Explanation:

Step1: Find the x - coordinate of the point

Use the section - formula for x - coordinate $x=\ x_1+\frac{m}{n}(x_2 - x_1)$. Here, $x_1=-4$, $x_2 = 6$, $m = 3$, $n=4$.
$x=-4+\frac{3}{4}(6-( - 4))=-4+\frac{3}{4}(10)=-4 + 7.5=3.5$

Step2: Find the y - coordinate of the point

Use the section - formula for y - coordinate $y=y_1+\frac{m}{n}(y_2 - y_1)$. Here, $y_1 = 3$, $y_2=-7$, $m = 3$, $n = 4$.
$y=3+\frac{3}{4}(-7 - 3)=3+\frac{3}{4}(-10)=3-7.5=-4.5$

Answer:

$(3.5,-4.5)$