Question

On a number line, the line segment from Q to S has endpoints Q at -68 and S at 53. Point R partitions the line segment from Q to S in a 10:3 ratio. Find the coordinate of point R. Round your answer to the nearest tenth if necessary.

Answer 1

To find the coordinate of point R on the number line given the endpoints Q and S, we can partition the line segment in a 10:3 ratio. The coordinate of point R can be found by multiplying the length of the entire line segment by the fraction 10/13 and adding it to the coordinate of Q. Therefore, the coordinate of point R is approximately 25.85.

Step-by-step explanation:

To find the coordinate of point R, we can use the concept of partitioning a line segment in a given ratio. The ratio given is 10:3. This means that the line segment from Q to R is 10/13 times the length of the entire line segment from Q to S. Therefore, the coordinate of point R can be found by calculating this fraction of the total distance and adding it to the coordinate of Q.

First, we need to find the length of the entire line segment from Q to S. This can be done by subtracting the coordinate of Q (-68) from the coordinate of S (53), which gives us 121.

Next, we can calculate the distance from Q to R by multiplying the length of the entire line segment (121) by the fraction 10/13. This gives us 93.85. Finally, we add this distance to the coordinate of Q (-68) to find the coordinate of point R, which is approximately -68 + 93.85 = 25.85.