If the mid-point of the line segment joining the points A (3, 4) and B (k, 6) is P (x, y) and x + y – 10 = 0, find the value of k

Solution:

Given, P(x, y) is the midpoint of the line segment joining the points A(3, 4) and B(k, 6).

The equation of the line is x + y - 10 = 0.

We have to find the value of k.

The coordinates of the mid-point of the line segment joining the points P (x₁ , y₁) and Q (x₂ , y₂) are [(x₁ + x₂)/2, (y₁ + y₂)/2]

The midpoint of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y)

[(3 + k)/2, (4 + 6)/2] = (x, y)

[(3 + k)/2, (10)/2] = (x, y)

[(3 + k)/2, 5] = (x, y)

So, x = 3 + k/2 and y = 5

Put the value of x and y in the given equation of the line,

(3 + k)/2 + 5 - 10 = 0

(3 + k)/2 - 5 = 0

(3 + k)/2 = 5

3 + k = 10

k = 10 - 3

k = 7

Therefore, the value of k is 7.

✦ Try This: If the mid-point of the line segment joining the points P(5, 9) and Q(k, 9) is A(x, y) and 2x - y + 11= 0, find the value of k.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.3 Sample Problem 1

Summary:

If the mid-point of the line segment joining the points A (3, 4) and B (k, 6) is P (x, y) and x + y – 10 = 0, the value of k is 7

☛ Related Questions: