Answer:
C) [tex]\sqrt{106}[/tex] units
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where [tex]a[/tex] and [tex]b[/tex] are side lengths of a right triangle and [tex]c[/tex] is the hypotenuse, the longest side of the right triangle.
The distance formula is similar to that of the Pythagorean Theorem which is [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points that you wish to find the distance between them in an (x,y) coordinate plane.
Here, we are given that [tex](x_1,y_1)[/tex] is [tex]P(-4,-6)[/tex] and [tex](x_2,y_2)[/tex] is [tex]Q(1,3)[/tex]. So, we can use the distance formula as described previously to find the positive distance between the two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(1-(-4))^2+(3-(-6))^2}[/tex]
[tex]d=\sqrt{(1+4)^2+(3+6)^2}[/tex]
[tex]d=\sqrt{(5)^2+(9)^2}[/tex]
[tex]d=\sqrt{25+81}[/tex]
[tex]d=\sqrt{106}[/tex]
[tex]d \approx 10.295630141[/tex]
Since all of the given answer choices are in radical form, then C is the correct answer. The distance between the two points is [tex]\sqrt{106}[/tex] units.
