Question

The coordinates of point P and Q are (4, -3) and (-1, 7). Find the coordinates of point R on the line segment such that PR/PQ is equal to 3/5. a) (2, -1) b) (1, 1) c) (2, -1), (1, 1) d) (3, 2)

Answer 1

In this case, the coordinates of point R are (1, 3).

None of the given options is correct

Step-by-step explanation:

To find the coordinates of point R on the line segment PQ such that the ratio of PR to PQ is 3/5, we can use the section formula.

Given:

• - Point P has coordinates (4, -3)
• - Point Q has coordinates (-1, 7)
• - The ratio PR:PQ is 3/5

The section formula for a line segment that is divided internally in the ratio m:n is:

(rx, ry) = ((mx₂ + nx₁) / (m + n), (my₂ + ny₁) / (m + n))

Here, x₁ and y₁ are the coordinates of point P, x₂ and y₂ are the coordinates of point Q, and m:n is the given ratio.

Plugging in the given values:

• - m = 3 (since PR:PQ = 3/5)
• - n = 2 (PQ is the whole segment, so if PR is 3 parts, Q is 2 parts, making it a total of 5 parts)
• - P(x₁, y₁) = (4, -3)
• - Q(x₂, y₂) = (-1, 7)

Using the section formula, we can find the coordinates of point R (rx, ry):

• rx = (3*(-1) + 2*4) / (3 + 2) = (-3 + 8) / 5 = 5 / 5 = 1
• ry = (3*7 + 2*(-3)) / (3 + 2) = (21 - 6) / 5 = 15 / 5 = 3

Therefore, the coordinates of point R are (1, 3).

In conclusion, the correct answer is not among the options provided. The coordinates of point R on the line segment PQ are (1, 3), which is not listed as one of the answer choices.