Question

Find the distance between the points p(sin theta/2,0), Q(0,cos theta/2,0)

Answer 1

Solution:

To solve this question, we have to know Distance Formula.

Let P(x₁, y₁) and Q(x₂, y₂) be two points on the Cartesian Plane. Then the distance between the two points is given as:

$\rm \longrightarrow Distance = \sqrt{ {(x_{2} -x_{1} )}^{2} + {(y_{2} - y_{1} )}^{2} }$

Here, the points are P(sin θ/2, 0) and Q(0, cos θ/2)

So, the distance between the points will be:

$\rm \longrightarrow Distance = \sqrt{ {(0 -\sin {}^{\theta}/_{2} )}^{2} + {(\cos {}^{\theta}/_{2}- 0)}^{2} }$

$\rm \longrightarrow Distance = \sqrt{ sin^{2}\dfrac{\theta}{2}+cos^{2}\dfrac{\theta}{2}}$

We know that:

$\rm \longrightarrow sin^{2}\dfrac{\theta}{2}+cos^{2}\dfrac{\theta}{2}=1$

Therefore:

$\rm \longrightarrow Distance = \sqrt{ 1}$

$\rm \longrightarrow Distance = 1\: unit.$

★ Therefore, the distance between the points P(sin θ/2, 0) and Q(0, cos θ/2) is 1 unit.

Answer:

• The distance between the points P(sin θ/2, 0) and Q(0, cos θ/2) is 1 unit.

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:

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

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:

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

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:

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

Answer 2

Step-by-step explanation:

This is the answer for the question given above i.e. PQ = 1/2 units.