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## OGQR 2020: Question No. 78

In a rectangular coordinate system, straight-line k passes through points (0, 0) and (3, 2). Which of the following are coordinates of a point on k?

## Solution

### Given

In this question, we are given

• In a rectangular coordinate system, straight line k passes through points (0, 0) and (3, 2).

### To Find

We need to determine

• Among the given choices, which one indicates the coordinates of a point on k.

### Approach & Working

As we know that straight line k passes through points (0, 0) and (3, 2), the equation of the line k must be

• y – 0 / x – 0 = 0-2 / 0 -3

Or,  y/x = 2/3

Or, 2x = 3y

Now, if a point is on the line k, it should satisfy the equation of the line.

Checking with the given options:

• (9, 4): 2x = 2 * 9 = 18 & 3y = 3 * 4 = 12, hence, 2x ≠ 3y
• (4, 9): 2x = 2 * 4 = 8 & 3y = 3 * 9 = 27, hence, 2x ≠ 3y
• (-4, 6): 2x = 2 * -4 = -8 & 3y = 3 * 6 = 18, hence, 2x ≠ 3y
• (-6, -9): 2x = 2 * -6 = -12 & 3y = 3 * -9 = -27, hence, 2x ≠ 3y
• (-6, -4): 2x = 2 * -6 = -12 & 3y = 3 * -4 = -12, hence, 2x = 3y

Hence, the correct answer is option E.

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