Question

Whats the distance between points C(0, 4), T(-6, -3)

a √(37)
b √(85)
c √(109)

Answer 1

$\text{The formula of the distance between points}\ A(x_A;\ y_A)\ \text{and}\ B(x_B;\ y_B):\\\\|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

$\text{We have:}\\C(0;\ 4);\ T(-6;-3)\\\\\text{substitute coordinates of the points to the formula:}\\\\|CT|=\sqrt{(-6-0)^2+(-3-4)^2}=\sqrt{(-6)^2+(-7)^2}=\sqrt{36+49}=\sqrt{85}$

$\text{Answer:}\ b.\ \sqrt{85}$