The Straight Lines — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines2 Marks
Question
By using the concept of slope, show that the points (-2, -1), (4, 0), (3, 3) and (-3, 2) are the vertices of a parallelogram.
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Answer
Let the vertices be A(-2, -1), B(4, 0), C(3, 3) and D(-3, 2). Using slope formula, $\text{m}=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1},$ we get: Slope of $\text{AB}(\text{m}_1)=\frac{0-(-1)}{4-(-2)}=\frac{1}{6}$ Slope of $\text{CD}(\text{m}_2)=\frac{2-3}{-3-3}=\frac{-1}{-6}=\frac{1}{6}$ $\Rightarrow\text{m}_1=\text{m}_2\Rightarrow\text{AB}||\text{CD}$ Also Slope of $\text{AD }(\text{m}_2)=\frac{2-(-1)}{-3-(-2)}=\frac{3}{-1}=-3$ Slope of $\text{BC }(\text{m}_4)=\frac{3-0}{3-4}=\frac{3}{-1}=-3$ $\Rightarrow\text{m}_3=\text{m}_4\Rightarrow\text{AD}||\text{BC}$ Hence, ABCD is a parallelogram.
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