Question

can anyone answer these questions of​

Answer 1

Given points:-

• P(-5, 7) and Q(-1, 3)

To find:-

• The distance between P and Q.

Solution:-

We know,

To find the distance between two points we have a formula called distance formula.

Distance formula is as follows:-

• $\sf{\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)}}$

We are given the points as:-

P(-5, 7) and Q(-1, 3)

Here,

$\sf{x_1 = -5\:and\:x_2 = -1}$

$\sf{y_1 = 7\:and\:y_2 = 3}$

Now putting the values in the formula,

= $\sf{\sqrt{[-1 - (-5)]^2 + [3 - 7]^2}}$

= $\sf{\sqrt{[-1+5]^2 + [-4]^2}}$

= $\sf{\sqrt{(4)^2 + 16}}$

= $\sf{\sqrt{16 + 16}}$

= $\sf{\sqrt{32}}$

= $\sf{4\sqrt{2}}$

Therefore the distance between point P and Q is 4√2 units.

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Additional Information!!

↦ What are $\bf{x_1\:and\:x_2}$

✓ $\sf{x_1}$ is the abscissa (or point on x-axis) for the first coordinate. $\sf{x_2}$ is the abscissa (or the point on x-axis) for the second coordinate.

↦What are $\bf{y_1\:and\:y_2}$

✓ $\sf{y_1}$ is the ordinate (or point on y-axis) for the first coordinate. $\sf{y_2}$ is the ordinate (or point in y-axis) for the second coordinate.

↦ Why is distance formula necessary?

✓ Distance formula is necessary as it gives the shortest distance between any two coordinates.

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Answer 2

$\huge \bf{ \underline{ \underline{ Given :-}}}$

P(-5, 7) and Q(-1, 3)

To find:-

The distance between P and Q.

$\huge \bf{ \underline{ \underline{Solution:-}}}$

We know,

To find the distance between two points we have a formula called distance formula.

Distance formula is as follows:-

$\bf\sf{\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)}}$

We are given the points as:-

P(-5, 7) and Q(-1, 3)

Here,

$\bf{x_1 = -5\:and\:x_2 = -1}$

$\bf{y_1 = 7\:and\:y_2 = 3}$

Now putting the values in the formula,

$\longrightarrow \: \bf{\sqrt{[-1 - (-5)]^2 + [3 - 7]^2}}$

$\longrightarrow \ \: \bf{\sqrt{[-1+5]^2 + [-4]^2}}$

$\longrightarrow \: \bf{\sqrt{(4)^2 + 16}}$

$\longrightarrow \: \bf{\sqrt{16 + 16}}$

$\longrightarrow\bf{\sqrt{32}}$

$\therefore \sf \: the \: distance \: between \: point \\ \sf \: P \: and \: Q \: is \: 4 \sqrt{2} units.$