Geometry Concepts and Formulas

This video tutorial covers various problems in coordinate geometry, including finding coordinates of points on lines, calculating the area of triangles, and understanding circle properties such as center, radius, and circumference. It also explains how to derive equations for tangent lines, plot points in 3D space, and calculate distances. Additionally, the video discusses the area of squares and circles, properties of equilateral triangles, and how to write equations for medians, perpendicular bisectors, and altitudes in triangles.

What is the x-coordinate of point B if it shares the same x-coordinate with point A on a vertical line?

• 0

• 1

• 3

• 2

How do you calculate the area of a right triangle?

• Base minus height

• Base times height

• One half base times height

• Base plus height

What is the formula to find the midpoint of a line segment?

• (x1 + x2, y1 + y2)

• (x1 - x2, y1 - y2)

• ((x1 + x2)/2, (y1 + y2)/2)

• ((x1 - x2)/2, (y1 - y2)/2)

What is the standard equation of a circle with center (h, k) and radius r?

• x^2 + y^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

• x^2 - y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

How do you find the slope of a line perpendicular to another line with slope m?

• 1/m

• m

• -m

• -1/m

What is the area of a triangle bounded by the x-axis, y-axis, and the line 4x + y = 8?

• 4 square units

• 8 square units

• 12 square units

• 16 square units

What is the distance formula in three dimensions?

• √((x2-x1)^2 + (y2-y1)^2)

• (x2-x1) - (y2-y1) - (z2-z1)

• √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

• (x2-x1) + (y2-y1) + (z2-z1)

How do you calculate the area of an equilateral triangle with side length s?

• s^2

• √3/4 * s^2

• 1/2 * s^2

• s^2/2

What is the equation of the median of a triangle?

• It passes through the midpoint of a side and the opposite vertex

• It is perpendicular to a side

• It is parallel to a side

• It bisects an angle

What is the slope of the perpendicular bisector of a line with slope 1/3?

• 3

• 1/3

• -1/3

• -3