Point \[$ R \$\] Divides \[$\overline{PQ}\$\] In The Ratio \[$ 1:3 \$\]. If The \[$ X \$\]-coordinate Of \[$ R \$\] Is \[$-1\$\] And The \[$ X \$\]-coordinate Of \[$ P \$\] Is

Feb 27, 2025 by ADMIN 176 views

Point R Divides Line Segment PQ in the Ratio 1:3

In geometry, the concept of a point dividing a line segment in a given ratio is a fundamental idea. In this article, we will explore the concept of a point dividing a line segment in the ratio 1:3 and how it can be used to find the coordinates of the point. We will also discuss the properties of the line segment and the point that divides it in the given ratio.

The problem states that point R divides line segment PQ in the ratio 1:3. This means that the distance from P to R is 1 part, and the distance from R to Q is 3 parts. We are also given that the x-coordinate of point R is -1 and the x-coordinate of point P is unknown.

A line segment is a set of points that lie on a straight line and have a fixed length. In this case, the line segment PQ has a fixed length, and point R divides it in the ratio 1:3. This means that the distance from P to R is 1/4 of the total length of the line segment, and the distance from R to Q is 3/4 of the total length.

To find the x-coordinate of point P, we can use the concept of similar triangles. Since point R divides the line segment PQ in the ratio 1:3, we can draw a line from R to a point on the line segment that is 1 part away from P. Let's call this point Q'. Since the line segment PQ is divided in the ratio 1:3, we know that the distance from P to Q' is 1/4 of the total length of the line segment.

We can use similar triangles to find the x-coordinate of point P. Since the line segment PQ is divided in the ratio 1:3, we know that the distance from P to Q' is 1/4 of the total length of the line segment. We can also draw a line from R to Q' and use the concept of similar triangles to find the x-coordinate of point P.

Let's call the x-coordinate of point P x. Since the line segment PQ is divided in the ratio 1:3, we know that the distance from P to Q' is 1/4 of the total length of the line segment. We can also draw a line from R to Q' and use the concept of similar triangles to find the x-coordinate of point P.

Since the line segment PQ is divided in the ratio 1:3, we know that the distance from P to Q' is 1/4 of the total length of the line segment. We can also draw a line from R to Q' and use the concept of similar triangles to find the x-coordinate of point P.

We can use the formula for similar triangles to find the x-coordinate of point P. The formula is:

x = (1/4) * (x - (-1))

We can simplify the formula by multiplying both sides by 4:

4x = x - (-1)

We can solve for x by adding 1 to both sides:

4x + 1 = x

We can subtract x from both sides to get:

3x + 1 = 0

We can subtract 1 from both sides to get:

3x = -1

We can divide both sides by 3 to get:

x = -1/3

In this article, we explored the concept of a point dividing a line segment in the ratio 1:3. We used the concept of similar triangles to find the x-coordinate of point P. We also used the formula for similar triangles to find the x-coordinate of point P. The x-coordinate of point P is -1/3.

A point is a set of coordinates that lie on a plane. In this case, the point R has coordinates (-1, y). The point P has coordinates (x, y).

The final answer is -1/3.
Point R Divides Line Segment PQ in the Ratio 1:3 - Q&A

In our previous article, we explored the concept of a point dividing a line segment in the ratio 1:3. We used the concept of similar triangles to find the x-coordinate of point P. In this article, we will answer some frequently asked questions about the concept of a point dividing a line segment in the ratio 1:3.

A: The concept of a point dividing a line segment in the ratio 1:3 means that the distance from P to R is 1 part, and the distance from R to Q is 3 parts.

A: To find the x-coordinate of point P, you can use the concept of similar triangles. Since point R divides the line segment PQ in the ratio 1:3, you can draw a line from R to a point on the line segment that is 1 part away from P. Let's call this point Q'. Since the line segment PQ is divided in the ratio 1:3, you know that the distance from P to Q' is 1/4 of the total length of the line segment.

A: The formula for finding the x-coordinate of point P is:

x = (1/4) * (x - (-1))

A: You can simplify the formula by multiplying both sides by 4:

4x = x - (-1)

A: You can solve for x by adding 1 to both sides:

4x + 1 = x

A: You can subtract x from both sides to get:

3x + 1 = 0

A: You can subtract 1 from both sides to get:

3x = -1

A: You can divide both sides by 3 to get:

x = -1/3

A: The x-coordinate of point P is -1/3.

A: The ratio of the line segment PQ is 1:3.

A: To find the y-coordinate of point P, you need to know the y-coordinate of point R. Since point R has coordinates (-1, y), you can use the concept of similar triangles to find the y-coordinate of point P.

A: You can use the concept of similar triangles to find the y-coordinate of point P by drawing a line from R to a point on the line segment that is 1 part away from P. Let's call this point Q'. Since the line segment PQ is divided in the ratio 1:3, you know that the distance from P to Q' is 1/4 of the total length of the line segment.

A: The formula for finding the y-coordinate of point P is:

y = (1/4) * (y - y)

A: You can simplify the formula by multiplying both sides by 4:

4y = y - y

A: You can solve for y by adding y to both sides:

4y + y = y

A: You can subtract y from both sides to get:

3y = 0

A: You can divide both sides by 3 to get:

y = 0

A: The y-coordinate of point P is 0.

In this article, we answered some frequently asked questions about the concept of a point dividing a line segment in the ratio 1:3. We also provided the formulas for finding the x-coordinate and y-coordinate of point P. The x-coordinate of point P is -1/3, and the y-coordinate of point P is 0.

The final answer is -1/3 and 0.