The shortest distance between P and Q is 9.4 units.
Solution:
The coordinate of P is (–4, –2).
The coordinate of Q is (4, 3).
Let [tex]x_1=-4, y_1=-2, x_2=4, y_2=3[/tex].
To find the shortest distance between P and Q:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the given values in the formula, we get
[tex]d=\sqrt{(4-(-4))^2+(3-(-2))^2}[/tex]
[tex]d=\sqrt{(4+4)^2+(3+2)^2}[/tex]
[tex]d=\sqrt{(8)^2+(5)^2}[/tex]
Using 8² = 64 and 5² = 25
[tex]d=\sqrt{64+25}[/tex]
[tex]d=\sqrt{89}[/tex]
d = 9.4
The shortest distance between P and Q is 9.4 units.
