Math, asked by sairithwikneelam04, 2 months ago

3. Find the distance between the points P(a+b, a-b) and Q(a-b, -a,-b)​

Answers

Answered by ritikrawat4532
0

Answer:

P(a+b, a

Step-by-step explanation:

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Answered by StormEyes
5

Solution!!

The concept of co-ordinate geometry has to be used here. The coordinates of two points are given in the question. We are asked to find the distance between the two points.

P(a+b , a-b)

Q(a-b , -a-b)

Now, let's use a suitable formula which is the distance formula to find the distance between the two points P and Q.

\sf Distance\:PQ=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

Here,

x₁ = a+b

x₂ = a-b

y₁ = a-b

y₂ = -a-b

\sf Distance\:PQ=\sqrt{(a-b-(a+b))^{2}+(-a-b-(a-b))^{2}}

When there is a - sign in front of an expression in parentheses, change the sign of each term in the expression.

\sf Distance\:PQ=\sqrt{(a-b-a-b)^{2}+(-a-b-a+b)^{2}}

Since two opposites add up to zero, remove them from the expression.

\sf Distance\:PQ=\sqrt{(-b-b)^{2}+(-a-a)^{2}}

Collect the like terms.

\sf Distance\:PQ=\sqrt{(-2b)^{2}+(-2a)^{2}}

To raise a product to a power, raise each factor to that power.

\sf Distance\:PQ=\sqrt{4b^{2}+4a^{2}}

Simplify the radical expression.

\sf Distance\:PQ=2\sqrt{b^{2}+a^{2}}

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