1.

The co-ordinates of a point P in 1 pointquadrant I are (8,y). If thedistance of P from origin is 10units, then the value of y isO 2 unitsO 4 uniteO6 unitsO 8units​

Answer»

\underline{\underline{\sf{\maltese\:\:Question}}}

  • The co-ordinates of a point P lying in Quadrant I are (8 , y). If the  distance of P from ORIGIN is 10  units, then the value of y is

\underline{\underline{\sf{\maltese\:\:Given}}}

  • The co-ordinates of a point P LYE in Quadrant I
  • The co-ordinates of a point P are (8 , y)
  • Distance of P from origin is 10  units

\underline{\underline{\sf{\maltese\:\:To\:Find}}}

  • Value of y

\underline{\underline{\sf{\maltese\:\:Answer}}}

  • y = 6 units

\underline{\underline{\sf{\maltese\:\:Calculations}}}

We know : In FIRST quadrant, both x and y co-ordinate are positive

Hence y will have a positive value

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Distance Between Two Points is given by : \sf{\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}}

Note : The Distance of Point P(x₁ , y₁) from Origin O(0,0) is OP = \sf{\sqrt{x_1\:^2+y_1\:^2}}

Coming to Question :

OP = \sf{\sqrt{x_1\:^2+y_1\:^2}}

⇒ 10 units = \sf{\sqrt{x_1\:^2+y_1\:^2}}

⇒ 10 units = \sf{\sqrt{8^2+y^2}}

⇒ 10 units = \sf{\sqrt{64+y^2}}

Squaring On Both Sides

⇒ (10)² units = \sf{(\sqrt{64+y^2})^2}

⇒ 100 units = 64 + y²

Subtracting 64 from Both Sides

⇒ 100 units - 64 = 64 + y² - 64

⇒ 36 units = y²

Switch Sides

⇒ y² = 36 units

Taking Root on Both Sides

⇒ √y² = ±√36 units

⇒ y = ±√36 units

⇒ y = + 6 units or - 6 units

We already came to know y will have a positive value

⇒ y = 6 units

\underline{\underline{\sf{\maltese\:\:Know\:More}}}

  • Co-ordinates of the origin is (0, 0).
  • The y-coordinates of every point on X-axis is zero
  • The x-coordinates of every point on Y-axis is zero.
  • Any point on X-axis is of the FORM (x, 0).
  • Any point on Y-axis is of the form (0, y).  
  • A line which is parallel to the X-axis is called a horizontal line. On the horizontal line. The y-coordinates of all the point are same.
  • A line which is parallel to the Y-axis is called a vertical line. On vertical line, the x-coordinates of all points are same.

________________________________________________________

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