Question

Design the vertices of a square RSTU are R(- 1.3); 5(3, 3); T(3, - 1) and U (-1,-1); overline LS Find on diagonal that is 3/4 distance S.

Answer 1

To find a point that lies three-fourths the distance on a diagonal of a square from one vertex, take the midpoint of the diagonal, calculate the vector from the given vertex to the midpoint, and then scale it by 3/4.

Step-by-step explanation:

The task involves finding a point on the diagonal of a square that is at a specific fraction of the distance from one vertex to another. To solve this, we need to utilize vector operations and a geometrical approach. Since a square's diagonals bisect each other, we can find the midpoint first, and then calculate the point that is 3/4 of the distance from one vertex to the midpoint. This involves finding the vector representing the diagonal and scalarily multiplying it by 3/4.

Procedure to Find the Point

1. Identify the vertices of the square: R(-1,3), S(3,3), T(3,-1), and U(-1,-1).
2. Find the midpoint of the diagonal RT, which will give us the center of the square.
3. From S, calculate the vector to the midpoint.
4. Multiply this vector by 3/4 to find the point on the diagonal ST that is three-fourths the distance from S.