Find the distance between each of the following pairs of points. P(-5, 7), Q(-1, 3)

Find the distance between each of the following pairs of points.

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

Answer:-

P(–5, 7), Q(–1, 3)

[PQ = sqrt{left( – 5 – left( – 1 right) right)^2 + left( 7 – 3 right)^2} = sqrt{left( – 4 right)^2 + 4^2}]

[ = sqrt{16 + 16}]

[ = 4sqrt{2}]

Explanation:- 

To find the distance between two points in a 2D plane, we use the distance formula, which is given by:

[PQ = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}]

where P(x1, y1) and Q(x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between the points P(-5, 7) and Q(-1, 3) as follows:

First, we substitute the coordinates of the two points into the distance formula to obtain:

[PQ = sqrt{(-1 – (-5))^2 + (3 – 7)^2}]

Next, we simplify the expression inside the square root by performing the subtraction and squaring operations:

[PQ = sqrt{(4)^2 + (-4)^2}]

We simplify further by performing the addition and square root operations:

[PQ = sqrt{16 + 16}]

[PQ = sqrt{32}]

Finally, we simplify by factoring out the largest perfect square, which is 16, from 32:

[PQ = sqrt{16 times 2}]

[PQ = sqrt{16} times sqrt{2}]

[PQ = 4sqrt{2}]

Therefore, the distance between the points P(-5, 7) and Q(-1, 3) is 4√2 units.