From the point (4, 3) a perpendicular is dropped on the X-axis as well as on the Y-axis. If the lengths of perpendiculars are p and q respectively, then which one of the following is correct?a)p = qb)3p = 4qc)4p = 3qd)p + q = 5Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Given Information:

- We are given a point (4, 3).
- A perpendicular is dropped from this point on the X-axis and Y-axis.
- The length of the perpendicular dropped on the X-axis is p.
- The length of the perpendicular dropped on the Y-axis is q.

Approach:

- To solve this problem, we will use the concept of distance formula and Pythagorean theorem.
- We will find the distance between the given point (4, 3) and the X-axis.
- Similarly, we will find the distance between the given point (4, 3) and the Y-axis.
- Using the Pythagorean theorem, we can relate the distances and calculate the values of p and q.

Solution:

Step 1: Finding the Distance between the Given Point and X-axis:

- The X-axis is a horizontal line passing through the origin, with all points having a y-coordinate of 0.
- To find the distance between the given point (4, 3) and the X-axis, we need to calculate the difference between the y-coordinate of the given point and the y-coordinate of any point on the X-axis.
- Since the y-coordinate of any point on the X-axis is 0, the difference will be |3 - 0| = 3.
- Therefore, the distance between the given point (4, 3) and the X-axis is p = 3.

Step 2: Finding the Distance between the Given Point and Y-axis:

- The Y-axis is a vertical line passing through the origin, with all points having an x-coordinate of 0.
- To find the distance between the given point (4, 3) and the Y-axis, we need to calculate the difference between the x-coordinate of the given point and the x-coordinate of any point on the Y-axis.
- Since the x-coordinate of any point on the Y-axis is 0, the difference will be |4 - 0| = 4.
- Therefore, the distance between the given point (4, 3) and the Y-axis is q = 4.

Step 3: Verifying the Correct Option:

- Now, we need to check which option is correct based on the values of p and q that we calculated.
- Option (a) states p = q, which is not true because p = 3 and q = 4.
- Option (b) states 3p = 4q, which is not true because 3p = 3 * 3 = 9 and 4q = 4 * 4 = 16.
- Option (c) states 4p = 3q, which is true because 4p = 4 * 3 = 12 and 3q = 3 * 4 = 12.
- Option (d) states p * q = 5, which is not true because p * q = 3 * 4 = 12.
- Therefore, the correct option is (c) 4p = 3q.

Therefore, the correct answer is option 'C' - 4p = 3q.

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