1. **Determine the distance between points I (14, 8) and J (8, -3).** The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ Substitute the values: $$d = \sqrt{(8 - 14)^2 + (-3 - 8)^2} = \sqrt{(-6)^2 + (-11)^2} = \sqrt{36 + 121} = \sqrt{157}$$ So, the distance is $\sqrt{157}$ units. 2. **Find the midpoint coordinates of segment TV where T (12, -5) and V (18, -3).** The midpoint formula is: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$ Calculate: $$M = \left(\frac{12 + 18}{2}, \frac{-5 + (-3)}{2}\right) = \left(\frac{30}{2}, \frac{-8}{2}\right) = (15, -4)$$ 3. **Write the equation of the circle with center at (0,0) passing through (2,5).** The center-radius form of a circle is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $(h,k)$ is the center and $r$ is the radius. Since center is $(0,0)$, the equation simplifies to: $$ x^2 + y^2 = r^2 $$ Find radius $r$ by distance from center to point (2,5): $$ r = \sqrt{(2 - 0)^2 + (5 - 0)^2} = \sqrt{4 + 25} = \sqrt{29} $$ Therefore, the equation is: $$ x^2 + y^2 = 29 $$