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The points (4, 5), (7, 6) and (6, 3) are collinear. Is the following statement true or false

Solution:

Consider the points A(4, 5), B (7, 6) and C (6, 3)

We know that

The distance between two points (x₁, y₁) and (x₂, y₂) is

d=\(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

First let us consider

AB = \(\sqrt{(7-4)^{2}+(6-5)^{2}}=\sqrt{9+1}=\sqrt{10}\)

BC = \(\sqrt{(6-7)^{2}+(3-6)^{2}}=\sqrt{1+9}=\sqrt{10}\)

AC = \(\sqrt{(6-4)^{2}+(3-5)^{2}}=\sqrt{4+4}=\sqrt{8}\)

If the points are collinear, AB + BC = AC

Let us substitute the values

√10 + √10 ≠√8

Therefore, the points are not collinear.

✦ Try This: The points (3, 4), (6, 5) and (5, 2) are collinear.

Consider the points A(3, 4), B (6, 5) and C (5, 2)

We know that

The distance between two points (x₁, y₁) and (x₂, y₂) is

d=\(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

First let us consider

AB = \(\sqrt{(6-3)^{2}+(5-4)^{2}}=\sqrt{9+1}=\sqrt{10}\)

BC = \(\sqrt{(5-6)^{2}+(2-5)^{2}}=\sqrt{1+9}=\sqrt{10}\)

AC = \(\sqrt{(5-3)^{2}+(2-4)^{2}}=\sqrt{4+4}=\sqrt{8}\)

If the points are collinear, AB + BC = AC

Let us substitute the values

√10 + √10 ≠√8

Therefore, the points are not collinear.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.2 Sample Problem 2

Summary:

The following statement is False since the points (4, 5), (7, 6) and (6, 3) are not collinear

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