Question

1. the ratio of fx to xk is 1:1. which point is located at x? 21. find the coordinate of q on fl such that the ratio of fq to ql is 12:7. refer to the number - line.

Explanation:

Step1: Identify the coordinates of endpoints for problem 20

Let the coordinate of $F=- 15$ and $K = - 1$. Since the ratio of $FX$ to $XK$ is $1:1$, $X$ is the mid - point of $FK$.

Step2: Use mid - point formula for problem 20

The mid - point formula for two points $a$ and $b$ on a number line is $M=\frac{a + b}{2}$. Here $a=-15$ and $b = - 1$. So $X=\frac{-15+( - 1)}{2}=\frac{-15 - 1}{2}=\frac{-16}{2}=-8$. The point at $X$ is $H$.

Step3: Identify the coordinates of endpoints for problem 21

Let the coordinate of $F=-15$ and $L = 5$. Let the coordinate of $Q$ be $x$. The ratio of $FQ$ to $QL$ is $12:7$.

Step4: Use the section formula for problem 21

The section formula for a point $Q$ that divides the line segment joining $F(x_1)$ and $L(x_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$. Here $x_1=-15$, $x_2 = 5$, $m = 12$ and $n = 7$. Then $x=\frac{12\times5+7\times(-15)}{12 + 7}=\frac{60-105}{19}=\frac{-45}{19}\approx - 2.37$.

Answer:

1. H
2. $\frac{-45}{19}$