Use your method (from Problem 6) to check if the points R (-5, -1),…

Question 18 of 25advanced🔧 ApplyLong Answer4 marks

Use your method (from Problem 6) to check if the points $R\,(-5,\,-1)$ , $B\,(-2,\,-5)$ and $C\,(4,\,-12)$ are on the same straight line. Now plot both sets of points and check your answers.

Correct Answer

The points $R$ , $B$ , and $C$ do not lie on the same straight line. When plotted, the first set of points ( $M$ , $A$ , $G$ ) forms a straight line, while the second set ( $R$ , $B$ , $C$ ) forms a triangle.

Exercise: END-OF-CHAPTER EXERCISES | Q: *7 | (Page 12)

For More Understanding

Explanation

The method from Problem 6 to check collinearity without plotting is to compare the slopes of the line segments formed by the points. If the slopes are equal, the points lie on the same straight line.

For points $R(-5,\,-1)$ , $B(-2,\,-5)$ , and $C(4,\,-12)$ , the slope of $RB$ is $-4/3$ and the slope of $BC$ is $-7/6$ . Since these slopes are not equal, the points are not collinear.

Plotting both sets of points visually confirms this: $M$ , $A$ , and $G$ fall on a line, while $R$ , $B$ , and $C$ form a triangle.

Solution Steps

Step 1: Use the slope method from Problem 6. If the slope between the first two points equals the slope between the next two points, the points lie on the same straight line.
Step 2: Calculate the slope of $RB$ :
$\frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-1)}{-2 - (-5)} = \frac{-4}{3}$
Step 3: Calculate the slope of $BC$ :
$\frac{-12 - (-5)}{4 - (-2)} = \frac{-7}{6}$
Step 4: Compare the slopes. Since $-4/3$ (or $-8/6$ ) is not equal to $-7/6$ , the points $R$ , $B$ , and $C$ do not lie on the same straight line.
Step 5: Plotting both sets of points on the Cartesian plane shows that $M(-3,\,-4)$ , $A(0,\,0)$ , and $G(6,\,8)$ fall on a straight line, while $R$ , $B$ , and $C$ form a triangle, confirming the answer.

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