Question

. If p(1/2 , x/2) is the midpoint of the line segment joiningthe points A(3, 7) and B(- 2, 4) then the value of x is​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given: P(1/2, x/2) is the midpoint of the line segment joining the points A(3, 7) and B(-2, 4).

→ To solve this, let us calculate the coordinates of midpoint of line segment AB.

The coordinates of midpoint of AB will be:

$\rm = \bigg( \dfrac{3 - 2}{2} , \dfrac{7 + 4}{2} \bigg)$

$\rm = \bigg( \dfrac{1}{2} , \dfrac{11}{2} \bigg)$

Also, P is the midpoint of AB. Therefore:

$\rm: \longmapsto P= \bigg( \dfrac{1}{2} , \dfrac{11}{2} \bigg)$

$\rm: \longmapsto \bigg( \dfrac{1}{2} , \dfrac{x}{2} \bigg)= \bigg( \dfrac{1}{2} , \dfrac{11}{2} \bigg)$

Comparing both sides, we get:

$\rm: \longmapsto \dfrac{x}{2} = \dfrac{11}{2}$

$\rm: \longmapsto x = 11$

★ So, the value of x is 11.

$\textsf{\large{\underline{Learn More}:}}$

1. Section formula.

Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the point which divides PQ internally in the ratio m₁ : m₂. Then, the coordinates of R will be:

$\rm:\longmapsto R = \bigg(\dfrac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}}, \dfrac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}\bigg)$

2. Mid-point formula.

Let P(x₁, y₁) and Q(x₂, y₂) be two points in the coordinate plane and R(x, y) be the mid-point of PQ. Then, the coordinates of R will be:

$\rm:\longmapsto R = \bigg(\dfrac{x_{1}+x_{2}}{2}, \dfrac{y_{1}+y_{2}}{2}\bigg)$

3. Centroid of a triangle.

Centroid of a triangle is the point where the medians of the triangle meet.

Let A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) be the vertices of a triangle. Let R(x, y) be the centroid of the triangle. Then, the coordinates of R will be:

$\rm:\longmapsto R = \bigg(\dfrac{x_{1}+x_{2}+x_{3}}{3}, \dfrac{y_{1}+y_{2}+y_{3}}{3}\bigg)$

Answer 2

Answer:

Given P is the mid point of AB,where A(−6,5) and B(−2,3)

∴  2a​=2−6+(−2)​

∴a=−8

Step-by-step explanation:

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