Coordinate Geometry (Advanced)

Harder items at competition-adjacent depth.

Phase 2 · ACT Math

Coordinate Geometry: core idea

Parallel/perpendicular slopes.

Find the equation of the perpendicular bisector of the segment from $(0,0)$ to $(6,4)$ .

Hint: Use midpoint and negative reciprocal slope. Answer: y=-3x/2+13/2.

1. A circle has equation $x^2+y^2-6x+8y-11=0$ . Find its radius.
2. Find the area of the triangle with vertices $(0,0),(8,0),(3,6)$ .
3. The line $2x+3y=12$ intersects the $x$ -axis at what point?
4. A dilation centered at origin with scale factor $-2$ maps $(3,-4)$ where?
5. Find the equation of a line through $(2,-3)$ parallel to $5x-2y=8$ .
6. A point on the $y$ -axis is equidistant from $(2,1)$ and $(6,5)$ . Find its $y$ -coordinate.
7. Find the area enclosed by $x=0$ , $y=0$ , and $2x+y=8$ .
8. The endpoints of a diameter are $(-2,5)$ and $(4,-3)$ . Write the circle's center.
9. Find the slope of a line tangent to $x^2+y^2=25$ at $(3,4)$ .