Question

Find the distance between each pair of points.

Answer 1

The distances are:

- E and F: 4 units.

- C and D: 5 units.

- G and H: 3 units.

- A and B: 6 units.

Why?

We can find the distance between each pair of points using the following formula:

$d(P_1,P_2)=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

So, calculating we have:

- E(-2, -1) and F(-2, -5):

$d(E,F)=\sqrt{(-2-(-2))^{2}+(-5-(-1))^{2}}\\\\d(E,F)=\sqrt{0+(-5+1)^{2}}=\sqrt{0+(-4)^{2}}=\sqrt{16}=4units$

- C(-4, 1) and D(1, 1):

$d(C,D)=\sqrt{(1-(-4))^{2}+(1-(1))^{2}}\\\\d(C,D)=\sqrt{(5)^{2}+0^{2}}=\sqrt{25+0}=\sqrt{25}=5units$

- G(3, -5) and H(6, -5):

$d(G,H)=\sqrt{(6-(3))^{2}+(-5-(-5))^{2}}\\\\d(G,H)=\sqrt{(3)^{2}+0^{2}}=\sqrt{9+0}=\sqrt{9}=3units$

- A(5, 4) and B( 5, -2):

$d(A,B)=\sqrt{(5-(5))^{2}+(-2-(4))^{2}}\\\\d(A,B)=\sqrt{0+(-6)^{2}}=\sqrt{0+36}=\sqrt{36}=6units$

Have a nice day!