Question

A line intersects the v-axis and x-axis at the points P and Q respectively. If (2,-5) is the
mid-point of PQ, then find the coordinates of P and Q.​

Answer 1

Answer :-

P(0, -10) and Q(4, 0)

Solution :-

A line intersect Y-axis and X-axis at P and Q respectively

Coordinates on Y-axis will be (0, y). So, let the coordinates on Y-axis be P(0, y)

Coordinates on X-axis will be (x, 0). So, let the coordinates on YlX-axis be Q(x, 0)

(2, - 5) is the the mid-point of P(y, 0) Q( y, 0)

Using mid-point formula

$\sf M(x ,y) = \bigg( \dfrac{x_1 + x_2 }{2} ,\dfrac{y_1 + y_2 }{2} \bigg)$

P(0, y) Q(x, 0) M(2, - 5)

Here,

• x1 = 0
• x2 = x
• y1 = y
• y2 = 0

Substituting the given values

$\implies \sf M(2 , - 5) = \bigg( \dfrac{0 + x}{2} ,\dfrac{ y + 0}{2} \bigg)$

$\implies \sf M(2 , - 5) = \bigg( \dfrac{x}{2} ,\dfrac{y }{2} \bigg)$

Equating X-coordinates

$\implies \sf 2 = \dfrac{x}{2}$

$\implies \sf x = 4$

Equating Y-coordinates

$\implies \sf - 5 = \dfrac{y}{2}$

$\implies \sf y = - 10$

Therefore the required coordinates are P( 0, - 10) and Q(4, 0).

Answer 2

Answer:

Step-by-step explanation:

Given :-

A line intersects the v-axis and x-axis at the points P and Q respectively.

If (2,-5) is the  mid-point of PQ.

To Find :-

Coordinates of P and Q

Formula to be used :-

Midpoint Formula = x = x₁ + x₂/2 and y = y₁ + y₂/2

Solution :-

Let the co-ordiantes of P be (x,y) and Q be (x₂y₂)

Midpoint of PQ = (2, −5)

Using midpoint formula,

$\implies\sf x = \dfrac{x_1 + x_2}{2} \: and \: y = \dfrac{y_1 + y_2}{2}\\\\\implies\sf 2 = \dfrac{x_1 + x_2}{2} \: and \:-5=\dfrac{y_1 + y_2}{2}\\\\\implies\sf x_1 + x_2 = 4\: and \:y_1 + y_2 = -10$

Since line PQ intersects the y-axis at P

Therefore, x₁ = 0 and y₂ = 0

Then, x₂ = 4 and y₁ = - 10

Hence, the co-ordinates of P are (0, −10) and Q are (4, 0).