Question

find the distance between the following pair of point (p-q,r-q) (p+q,q+r)

Answer 1

Distance = Whole square root of {(p+q)-(p-q)}^2 +{(q+r)-(r-q)}^2

⇒ Whole square root of {4q²+4q²}

⇒√8q²

⇒2q√2

Answer 2

The distance between the pair of points is $2q\sqrt{2}$ units.

Given:

P1 (p-q,r-q)

P2 (p+q,q+r)

To Find:

The distance between the pair of points.

Solution:

We know the formula,

d = $\sqrt[]{(x2-x1)^{2} +(y2 - y1)^{2} }$ ----------> (1)

x1 = p-q , x2 = p+q

y1 = r-q , y2 =q+r

substitute in equation (1)

  = $\sqrt[]{(p+q-p+q)^{2} +(q+r - r+q)^{2} }$

  = $\sqrt[]{(2q)^{2} +(2q)^{2} }$

  = $\sqrt[]{8q^{2} }$

  =$2q\sqrt{2}$ units

Therefore, The distance between the pair of points is $2q\sqrt{2}$ units.

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