Class 10th Math | Answer Key 2025 | PYQ 2025 | Question Paper Code 30-6-1 | Set 1 | CBSE Board | Q23

Summary

The video script explains a mathematical problem involving the coordinates of point P, and the distances from point P to two fixed points, A and B. Using the distance formula, the script demonstrates how to equate the distances and solve for the relationship between the coordinates of point P. Through algebraic manipulation, it is proven that the x-coordinate of point P is greater than the y-coordinate by a factor of two. The process includes applying the distance formula, squaring both sides, and simplifying the expressions to arrive at the final conclusion.

Takeaways

• 😀 The script begins by introducing a mathematical problem involving point P and its relationship with points A and B.
• 😀 The goal is to prove a relationship between the x and y coordinates of point P.
• 😀 Point A has coordinates (a, b), and point B has coordinates (x, y), while point P has coordinates (x', y').
• 😀 The distances from point P to points A and B are calculated using the distance formula.
• 😀 The distance formula for point P to point A is: sqrt((x' - a)^2 + (y' - b)^2).
• 😀 The distance formula for point P to point B is: sqrt((x' - x)^2 + (y' - y)^2).
• 😀 It is given that the distances from point P to points A and B are equal, which leads to equating the two distance formulas.
• 😀 Both sides of the equation are squared to eliminate the square roots, simplifying the equation.
• 😀 After expanding both sides, terms involving x' and y' are moved to one side of the equation for further simplification.
• 😀 The equation is then simplified to express a relationship between the coordinates of points A, B, and P.
• 😀 The script concludes with the proof showing that the x and y coordinates of point P satisfy the desired relationship.

Q & A

What is the problem stated in the script?

The problem is related to proving a relationship involving the coordinates of a point P, specifically proving that the x-coordinate of point P is greater than the y-coordinate.

What is the main goal in this exercise?

The main goal is to prove a relationship involving the coordinates of point P, where you need to show that the x-coordinate of P is greater than the y-coordinate.

How is the distance from point P to point A described in the script?

The distance from point P to point A is represented as 'x', which is the difference between the x-coordinates of points P and A, calculated using the distance formula.

What method is applied to find the distance between points?

The distance formula (also known as the Pythagorean theorem in two dimensions) is used to find the distance between points P and A, and between points P and B.

How is the distance between point P and point B represented?

The distance between point P and point B is represented as 'y', and is calculated similarly to the distance from point P to point A using the distance formula.

What is the key observation made when comparing the distances?

The key observation is that if the square roots of both distances are equal, then the values inside the square roots must also be equal.

What is the significance of squaring both sides of the equation?

Squaring both sides allows for the cancellation of the square roots, making it easier to solve the equation and find the relationship between the coordinates.

What mathematical operations are performed to solve the equation?

The operations involve expanding the squared terms, simplifying the equation, and eventually factoring to solve for the coordinates of point P.

What conclusion is reached regarding the x-coordinate and y-coordinate of point P?

The conclusion is that the x-coordinate of point P is greater than the y-coordinate, as the solution to the equation reveals a relationship where the x-coordinate exceeds the y-coordinate.

What is the final result after simplifying the equation?

After simplifying the equation, it is determined that the x-coordinate of point P is greater than the y-coordinate, which was the goal of the proof.