point b on a segment with endpoints a(2, -1) and c(4, 2) partitions the segment in a 1:3 ratio. find b.
(0.5, 0.75)
(-0.25, 2.5)
(0.75, 0.5)
(2.5, -0.25)

Question

Accepted Answer

# Explanation:
## Step1: Recall section - formula
If a point $B(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $C(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1 = 2,y_1=-1,x_2 = 4,y_2 = 2,m = 1,n = 3$.
## Step2: Calculate the $x$ - coordinate of $B$
$$
\begin{align*}
x&=\frac{1\times4+3\times2}{1 + 3}\
&=\frac{4 + 6}{4}\
&=\frac{10}{4}=2.5
\end{align*}
$$
## Step3: Calculate the $y$ - coordinate of $B$
$$
\begin{align*}
y&=\frac{1\times2+3\times(-1)}{1 + 3}\
&=\frac{2-3}{4}\
&=-\frac{1}{4}=-0.25
\end{align*}
$$

# Answer:
D. $(2.5,-0.25)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall section - formula

Step2: Calculate the \(x\) - coordinate of \(B\)

Step3: Calculate the \(y\) - coordinate of \(B\)

Answer: