Q. 5 - Geometry

Question

Tell whether each expression is positive or negative for the line shown:

$\begin{array}{l}a.y_2-y_1\\ b.x_2-x_1\\ c.\frac{y_2-y_1}{x_2-x_1}\end{array}$

Step-by-Step Solution

Answer

1. The expression$y_2-y_1$ is negative.
2. The expression $x_2-x_1$is positive.

The expression$\frac{y_2-y_1}{x_2-x_1}$ is negative.

Part a. Step-1 – Given

The given figure is:

Step-2 – To determine

We have to find whether given expression $y_2-y_1$ positive or negative.

Step-3 – Calculation

From the given figure we see that the coordinate $\left(x_2,y_2\right)$is in the fourth quadrant and $\left(x_1,y_1\right)$is in the second quadrant. 

So$x_2,y_1$ are positive values and$x_2,y_1$ are negative values.

It means, the value of expression$y_2-y_1$ is negative.

Because$-ve-(+ve)=-ve-ve=-ve$ .

So, the expression$y_2-y_1$ is negative.

Part b. Step-1 – Given

The given figure is:

Step-2 – To determine

We have to find whether given expression $x_2-x_1$ positive or negative.

Step-3 – Calculation

From the given figure we see that the coordinate$\left(x_2,y_2\right)$ is in the fourth quadrant and$\left(x_1,y_1\right)$ is in the second quadrant. 

So$x_2,y_1$ are positive values and$y_2,x_1$ are negative values.

It means, the value of expression$x_2-x_1$ is positive.

Because$+ve-(-ve)=+ve+ve=+ve$ .

So, the expression$x_2-x_1$ is positive.

Part c. Step-1 – Given

The given figure is:

Step-2 – To determine

We have to find whether given expression $\frac{y_2-y_1}{x_2-x_1}$ positive or negative.

Step-3 – Calculation

From part a, the expression$y_2-y_1$ is negative.

From part b, the expression$x_2-x_1$ is positive.

So, $\frac{y_2-y_1}{x_2-x_1}=\frac{-ve}{+ve}=-ve$.

It means$\frac{y_2-y_1}{x_2-x_1}$ is negative.