Question

If the coordinates of two points are a(3,4), b (5,-2) and a point p (x,5) is such that pa = pb, then find the area of pab

Answer 1

p(16,5) and area is 40square units

Answer 2

The value of x is 16. Area of triangle is 40 square units.

Step-by-step explanation:

It is given that the coordinates of two points are a(3,4), b(5,-2) and a point p (x,5) is such that pa = pb.

Distance formula:

$d=\sqrt{(x_2-x_1)^2-(y_2-y_1)^2}$

$pa=pb$

Using distance formula we get

$\sqrt{(x-3)^2+(5-4)^2}=\sqrt{(x-5)^2+(5-(-2))^2}$

$\sqrt{x^2 - 6 x + 10}=\sqrt{x^2 - 10 x + 74}$

Taking square on both sides.

$x^2 - 6 x + 10=x^2 - 10 x + 74$

Cancel out common factors.

$- 6 x + 10=- 10 x + 74$

$-6x+10x=74-10$

$4x=64$

$x=16$

The value of x is 16.

Area of triangle is

$A=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

The vertices of triangle pab are p(16,5), a(3,4) and b(5,-2). So, area of triangle is

$A=\dfrac{1}{2}|16(4-(-2))+3(-2-5)+5(5-4)|$

$A=\dfrac{1}{2}|96-21+5|$

$A=\dfrac{1}{2}|80|$

$A=\dfrac{1}{2}(80)$

Therefore, the value of x is 16. Area of triangle is 40 square units.

#Learn more

Find the area of the triangle formed by the points (1,2),(3,-4) and - 2,0).

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