Question

select an equation that can be used to find the coordinate of point k that is $\frac{2}{5}$ of the distance from q to r.
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
q r
a) $k=-2+\frac{2}{5}4 - (-2)$
b) $k=-3+\frac{2}{5}(4 - 3)$
c) $k=-3 + 4(\frac{2}{5}-3)$
d) $k=-3+\frac{2}{5}4 - (-3)$

Explanation:

Step1: Recall the section - formula for one - dimensional case

The formula to find a point \(K\) that is \(m/n\) of the distance from a point \(Q(x_1)\) to a point \(R(x_2)\) is \(K=x_1+\frac{m}{n}(x_2 - x_1)\).

Step2: Identify \(x_1\), \(x_2\), \(m\) and \(n\) values

From the number - line, \(x_1=-3\) (coordinate of \(Q\)), \(x_2 = 4\) (coordinate of \(R\)), \(m = 2\) and \(n=5\).

Step3: Substitute values into the formula

Substitute \(x_1=-3\), \(x_2 = 4\), \(m = 2\) and \(n = 5\) into the formula \(K=x_1+\frac{m}{n}(x_2 - x_1)\). We get \(K=-3+\frac{2}{5}[4-(-3)]\).

Answer:

D. \(K=-3+\frac{2}{5}[4 - (-3)]\)