Question

a lady bug crawls up a line segment starting at point a. where will it be when its $\frac{3}{4}$ of the way to point b? (5, 12) (45, 36)

Explanation:

Step1: Find x - coordinate formula

The formula for the x - coordinate of a point that is $t$ of the way from $(x_1,y_1)$ to $(x_2,y_2)$ is $x=x_1 + t(x_2 - x_1)$. Here, $x_1 = 5$, $x_2=45$, and $t=\frac{3}{4}$.
$x=5+\frac{3}{4}(45 - 5)$

Step2: Calculate x - coordinate

$x=5+\frac{3}{4}\times40=5 + 30=35$

Step3: Find y - coordinate formula

The formula for the y - coordinate of a point that is $t$ of the way from $(x_1,y_1)$ to $(x_2,y_2)$ is $y=y_1 + t(y_2 - y_1)$. Here, $y_1 = 12$, $y_2 = 36$, and $t=\frac{3}{4}$.
$y=12+\frac{3}{4}(36 - 12)$

Step4: Calculate y - coordinate

$y=12+\frac{3}{4}\times24=12 + 18=30$

Answer:

$(35,30)$