Mathematics

The mid-point of the line segment joining A(2, p) and B(q, 4) is (3, 5). Calculate the values of p and q.

Section Formula

29 Likes

Answer

Given, (3, 5) is the mid-point of A(2, p) and B(q, 4).

By mid-point formula,

$\Rightarrow 3 = \dfrac{(2 + q)}{2} \text{ and } 5 = \dfrac{(p + 4)}{2} \\[1em] \Rightarrow 2 + q = 6 \text{ and } p + 4 = 10 \\[1em] \Rightarrow q = 4 \text{ and } p = 6.$

Hence, p = 6 and q = 4.

Answered By

13 Likes

Mathematics

The mid-point of the line segment joining A(2, p) and B(q, 4) is (3, 5). Calculate the values of p and q.

Section Formula

Answer

Related Questions

P and Q are the points on the line segment joining the points A(3, -1) and B(-6, 5) such that AP = PQ = QB. Find the coordinates of P and Q.

The center of a circle is (α + 2, α - 5). Find the value of α, given that the circle passes through points (2, -2) and (8, -2).

The ends of a diameter of a circle have the coordinates (3, 0) and (-5, 6). PQ is another diameter where Q has the coordinates (-1, -2). Find the coordinates of P and the radius of the circle.

In what ratio does the point (-4, 6) divide the line segment joining the points A(-6, 10) and B(3, -8) ?