Flashcards: Coordinate Geometry Applications — 19 cards

What is the formula for distance between points $(x_1,y_1)$ and $(x_2,y_2)$?

$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

What is the distance between points I=(5,0) and N=(0,-6)?

$\sqrt{61}$ units

When are three points considered collinear based on distances?

When the sum of two consecutive distances equals the distance between the outer points.

What is the distance AB for points A=(-2,0) and B=(4,8)?

AB is 10 units.

Are points A=(-2,0), B=(4,8), and C=(4,-12) collinear?

No, because AB plus BC does not equal AC.

What are the distances AB and AR for points A=(0,0), B=(6,8), R=(-3,-4)?

Both distances AB and AR are 10 units.

What type of triangle is formed by points A=(0,0), B=(6,8), and R=(-3,-4)?

An isosceles triangle.

What are the distances QA and QB for points Q=(0,0), A=(-4,0), B=(0,4)?

Both distances QA and QB are 4 units.

What type of triangle is formed by points Q=(0,0), A=(-4,0), and B=(0,4)?

A right-angled isosceles triangle.

What is the formula for the midpoint of points $(x_1,y_1)$ and $(x_2,y_2)$?

$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

What is the midpoint of points S=(-3,0) and T=(3,0)?

M=(0,0)

What is the first step to find an unknown midpoint coordinate?

Substitute known endpoint coordinates into the midpoint formula.

After substituting known coordinates, what is the next step to find an unknown midpoint coordinate?

Form the corresponding equation.

What is the final step to find an unknown midpoint coordinate after forming the equation?

Solve for the unknown coordinate.

When is a point inside a circle centered at the origin?

When its distance from the origin is less than the radius.

When is a point outside a circle centered at the origin?

When its distance from the origin is greater than the radius.

What is the distance from the origin to point D=(5,6)?

The distance is √61.

Does point D=(5,6) lie inside the circle of radius √65?

Yes, because √61 is less than √65.

What is the distance between points (100,150) and (250,230)?

170 pixels