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ICSE Class 10 Mathematics Question 22 of 49

Multiple-Choice Questions — Question 22

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Question 22

In the given diagram, O is the origin and P is the mid-point of AB. The equation of OP is :

  1. y = x

  2. 2y = x

  3. y = 2x

  4. y = -x

In the given diagram, O is the origin and P is the mid-point of AB. The equation of OP is : Maths Competency Focused Practice Questions Class 10 Solutions.
Answer

From graph,

A = (4, 0) and B = (0, 2).

Given,

P is the mid-point of AB.

P = (4+02,0+22)=(42,22)\Big(\dfrac{4 + 0}{2}, \dfrac{0 + 2}{2}\Big) = \Big(\dfrac{4}{2}, \dfrac{2}{2}\Big) = (2, 1).

By two-point form,

⇒ y - y1 = y2−y1x2−x1(x−x1)\dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)

⇒ y - 1 = 1−02−0(x−2)\dfrac{1 - 0}{2 - 0}(x - 2)

⇒ y - 1 = 12(x−2)\dfrac{1}{2}(x - 2)

⇒ 2(y - 1) = x - 2

⇒ 2y - 2 = x - 2

⇒ 2y = x - 2 + 2

⇒ 2y = x.

Hence, Option 2 is the correct option.