NCERT Class X Chapter 7: Coordinate Geometry Exercise 7.2 Question 1
NCERT Class X Chapter 7: Coordinate Geometry
Question:
Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.
Given:
Points: \( A = (-1, 7) \), \( B = (4, -3) \)
Ratio: \( 2 : 3 \)
To Find:
The coordinates of the point dividing \( AB \) in the ratio \( 2 : 3 \).
Formula:
Section formula: If a point \( P \) divides the line segment joining \( (x_1, y_1) \) and \( (x_2, y_2) \) in the ratio \( m : n \), then the coordinates of \( P \) are:
$$ x = \frac{m x_2 + n x_1}{m + n}, \quad y = \frac{m y_2 + n y_1}{m + n} $$
Solution:
Step 1: Let the required point be \( P(x, y) \). Identify the values to substitute:
\( (x_1, y_1) = (-1, 7) \),
\( (x_2, y_2) = (4, -3) \),
\( m = 2, \ n = 3 \)
Step 2: Apply the section formula for the x-coordinate:
$$ x = \frac{m x_2 + n x_1}{m + n} = \frac{2 \times 4 + 3 \times (-1)}{2 + 3} $$Step 3: Simplify the x-coordinate:
$$ x = \frac{8 + (-3)}{5} = \frac{5}{5} = 1 $$Step 4: Apply the section formula for the y-coordinate:
$$ y = \frac{m y_2 + n y_1}{m + n} = \frac{2 \times (-3) + 3 \times 7}{2 + 3} $$Step 5: Simplify the y-coordinate:
$$ y = \frac{-6 + 21}{5} = \frac{15}{5} = 3 $$Result:
Therefore, the coordinates of the required point are \( (1, 3) \).
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