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Coordinate Geometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
Question
State whether the following statements are true or false. Justify your answer.
Points A(3, 1), B(12, -2) and C(0, 2) cannot be the vertices of a triangle.
✓

Answer

True:Points A, B, C can form a triangle if the sum of any two sides is greater than the third side.
$\Rightarrow AB^2 = (x_2- x_1)^2 + (y_2- y_1)^2$
$\Rightarrow AB^2 = (12 - 3)^2 + (-2 - 1)^2$
$\Rightarrow AB^2 = 81 + 9$
$\Rightarrow AB^2= 90$
$\Rightarrow\text{AB}=3\sqrt{10}\text{ units}$
$\Rightarrow BC^2 = (0 - 12)^2 + [2 - (-2)]^2$
$\Rightarrow BC^2= 144 + 16$
$\Rightarrow BC^2 = 160$
$\Rightarrow\text{BC}=4\sqrt{10}\text{ units}$
$\Rightarrow AC^2 = (0 - 3)^2 + (2 - 1)^2$
$\Rightarrow AC^2 = 9 + 1$
$\Rightarrow AC^2 = 10$
$\Rightarrow\text{AC}=\sqrt{10}\text{ units}$
$\therefore\text{AC}=\sqrt{10}\text{ units},\text{AB}=3\sqrt{10}\text{ units}$
and $\text{BC}=4\sqrt{10}\text{ units}$
Now, $\text{AB}+\text{AC}$
$\Rightarrow\sqrt{10}+3\sqrt{10}$
$\Rightarrow4\sqrt{10}\text{ units}=\text{BC}$
So, A, B, C points cannot from a $\triangle.$

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