Flashcards for:
Essential Concepts in Coordinate Geometry

Both a perpendicular bisector and altitude are perpendicular to the line segment they interact with.

The area of a right triangle with base 4 units and height 3 units is 6 square units.

To calculate the area enclosed by curves and lines or the shaded area between shapes, use applicable formulas and integrate over the given region.

Points on a vertical line share the same x-coordinate. For example, if Point A has coordinates (1,3) and Point C has coordinates (1,5), then Point B on the same vertical line shares the x-coordinate of 1 with A and C.

The coordinates for the center of the circle using the given points (1,2) and (7,10) can be calculated as (4,6) using the midpoint formula.

A median to a segment connects a vertex with the midpoint of the opposite side.

The standard equation of a circle with center (4,6) and radius 5 units is (x - 4)² + (y - 6)² = 25.

The radius of the circle with center at (4,6) and passing through points (1,2) and (7,10) can be found using the distance formula as 5 units.

The area of a right triangle is calculated as 0.5 * base * height.

The equation of a tangent line to a circle is perpendicular to the radius at the point of contact.

The equation of a line perpendicular to the line passing through A(3,2) and B(5,8) and passing through point B can be derived using the negative reciprocal of the slope and point-slope formula.

The Distance Formula in 3D is sqrt((x2 - x1)² + (y2 - y1)² + (z2 - z1)²).

The standard equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

The equation of the tangent line passing through points A(3,2) and B(5,8) can be derived using slope and point-slope formula as y = (-1/3)x + 29/3.

The distance from a point to a line is calculated using |Ax1 + By1 + C| / sqrt(A² + B²).

The center of a circle can be found using the midpoint formula: ((x1 + x2) / 2, (y1 + y2) / 2).