Fractional distance formula and distance formula review

Front

What is the fractional distance formula?

Back

The fractional distance formula is used to find a point that divides a line segment into a specific ratio. If point P divides segment AB in the ratio m:n, the coordinates of P can be calculated as: P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right).

Front

How do you find a point that is \frac{2}{5} the distance from A to B?

Back

To find a point that is \frac{2}{5} the distance from A to B, use the fractional distance formula with m=2 and n=3 (since 2+3=5).

Front

If point W is on line segment AB such that AW = \frac{2}{5}AB, what fraction represents WB?

Back

WB = \frac{3}{5}AB, since AW + WB = AB.

Front

What is the distance formula in a coordinate plane?

Back

The distance formula is given by: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, where (x_1, y_1) and (x_2, y_2) are the coordinates of the two points.

Front

If point Q is \frac{3}{4} the distance from A to B, how do you calculate its coordinates?

Back

Use the fractional distance formula with m=3 and n=1 (since 3+1=4) to find the coordinates of point Q.

Front

What does it mean for a point to be \frac{7}{10} the distance from E to F?

Back

It means that the point is located closer to F than E, specifically at a distance that is 70% of the total distance EF.

Front

How do you determine the coordinates of a point that is \frac{5}{7} the distance from D to C?

Back

Apply the fractional distance formula with m=5 and n=2 (since 5+2=7) to find the coordinates.

Front

What is the significance of the ratio in the fractional distance formula?

Back

The ratio determines how the total distance is divided between the two points, affecting the location of the dividing point.

Front

If the coordinates of A are (x1, y1) and B are (x2, y2), how do you find the coordinates of a point that is \frac{1}{2} the distance from A to B?

Back

Use the formula: P = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right).

Front

What is the relationship between the distances AW, WB, and AB?

Back

AW + WB = AB, where AW is the distance from A to W, WB is the distance from W to B, and AB is the total distance from A to B.