Question

find the distance between the pointe PC-6,4)
and a (-1, -5).​

Answer 1

Answer:

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Answer 2

Answer :

$\large{\star\:\:\boxed{\bf{PC\:=\:\sqrt{106}\:\:units} } \:\:\star}$

Explanation :

Given :–

• P(-6 , 4) and C(-1 , -5) are points on the x-y co-ordinate plane .

To Find :–

• The Distance between P(-6 , 4) and C(-1 , -5)

Formula Applied :–

• $\boxed{\bf{\star\:\:d\:=\:\sqrt{{(x_2\:-\:x_1)}^2\:+\:{(y_2\:-\:y_1)}^2} \:\:\star}}$

Solution :–

Let (-6 , 4) be (x₁ , y₁) and (-1 , -5) be (x₂ , y₂) .

Putting these values in the Formula :

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

$\rightarrow\sf{PC\:=\:\sqrt{{(-1\:-\:(-6))}^2\:+\:{(-5\:-\:4)}^2}}$

$\rightarrow\sf{PC\:=\:\sqrt{{(-1\:+\:6)}^2\:+\:{(-9)}^2}}$

$\rightarrow\sf{PC\:=\:\sqrt{{(5)}^2\:+\:81}}$

$\rightarrow\sf{PC\:=\:\sqrt{25\:+\:81}}$

$\rightarrow\sf{PC\:=\:\sqrt{106}\:\:units}$

∴ The Distance between P and C is 10.3 Units (approx.) .