for Sumi's shop
Partitioning a Directed Line Segment — Easy Worksheet 1
Grade 10 · MathSheets Name: ____________________ Date: __________
A point P that divides AB in the ratio m:n has AP:PB = m:n, measured from A toward B. Write points as ordered pairs like (3, -2) and ratios like 2:3.
How to solve
A ratio m:n splits the segment into m + n equal parts, and P is m of those parts away from A. So P is mm + n of the way from A to B. On a number line: P = a + mm + n · (b - a). On the coordinate plane, do the same thing for the x-coordinates and again for the y-coordinates. Example: A(1, 2), B(11, 7), ratio 2:3. P is 25 of the way: x = 1 + 25 · 10 = 5 and y = 2 + 25 · 5 = 4, so P is (5, 4).
Example
Point P divides AB in the ratio 3:1. What fraction of the way from A to B is P?
Answer: 34
✓ Correct!
Not quite. The answer is
💡 How to solve: Partitioning a Directed Line Segment
A ratio m:n splits the segment into m + n equal parts, and P is m of those parts away from A. So P is mm + n of the way from A to B. On a number line: P = a + mm + n · (b - a). On the coordinate plane, do the same thing for the x-coordinates and again for the y-coordinates. Example: A(1, 2), B(11, 7), ratio 2:3. P is 25 of the way: x = 1 + 25 · 10 = 5 and y = 2 + 25 · 5 = 4, so P is (5, 4).
Try a similar one
On a number line, A is at 10 and B is at 18. Point P is 14 of the way from A to B. Find the coordinate of P.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Partitioning a Directed Line Segment
A ratio m:n splits the segment into m + n equal parts, and P is m of those parts away from A. So P is mm + n of the way from A to B. On a number line: P = a + mm + n · (b - a). On the coordinate plane, do the same thing for the x-coordinates and again for the y-coordinates. Example: A(1, 2), B(11, 7), ratio 2:3. P is 25 of the way: x = 1 + 25 · 10 = 5 and y = 2 + 25 · 5 = 4, so P is (5, 4).
Try a similar one
Point P divides AB in the ratio 3:1. What fraction of the way from A to B is P?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Partitioning a Directed Line Segment
A ratio m:n splits the segment into m + n equal parts, and P is m of those parts away from A. So P is mm + n of the way from A to B. On a number line: P = a + mm + n · (b - a). On the coordinate plane, do the same thing for the x-coordinates and again for the y-coordinates. Example: A(1, 2), B(11, 7), ratio 2:3. P is 25 of the way: x = 1 + 25 · 10 = 5 and y = 2 + 25 · 5 = 4, so P is (5, 4).
Try a similar one
Point P divides AB in the ratio 3:1. What fraction of the way from A to B is P?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Partitioning a Directed Line Segment
A ratio m:n splits the segment into m + n equal parts, and P is m of those parts away from A. So P is mm + n of the way from A to B. On a number line: P = a + mm + n · (b - a). On the coordinate plane, do the same thing for the x-coordinates and again for the y-coordinates. Example: A(1, 2), B(11, 7), ratio 2:3. P is 25 of the way: x = 1 + 25 · 10 = 5 and y = 2 + 25 · 5 = 4, so P is (5, 4).
Try a similar one
Point P divides AB in the ratio 1:2. What fraction of the way from A to B is P?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Partitioning a Directed Line Segment
A ratio m:n splits the segment into m + n equal parts, and P is m of those parts away from A. So P is mm + n of the way from A to B. On a number line: P = a + mm + n · (b - a). On the coordinate plane, do the same thing for the x-coordinates and again for the y-coordinates. Example: A(1, 2), B(11, 7), ratio 2:3. P is 25 of the way: x = 1 + 25 · 10 = 5 and y = 2 + 25 · 5 = 4, so P is (5, 4).
Try a similar one
Point P divides AB in the ratio 1:2. What fraction of the way from A to B is P?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Partitioning a Directed Line Segment
A ratio m:n splits the segment into m + n equal parts, and P is m of those parts away from A. So P is mm + n of the way from A to B. On a number line: P = a + mm + n · (b - a). On the coordinate plane, do the same thing for the x-coordinates and again for the y-coordinates. Example: A(1, 2), B(11, 7), ratio 2:3. P is 25 of the way: x = 1 + 25 · 10 = 5 and y = 2 + 25 · 5 = 4, so P is (5, 4).
Try a similar one
Point P divides AB in the ratio 3:1. What fraction of the way from A to B is P?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Partitioning a Directed Line Segment
A ratio m:n splits the segment into m + n equal parts, and P is m of those parts away from A. So P is mm + n of the way from A to B. On a number line: P = a + mm + n · (b - a). On the coordinate plane, do the same thing for the x-coordinates and again for the y-coordinates. Example: A(1, 2), B(11, 7), ratio 2:3. P is 25 of the way: x = 1 + 25 · 10 = 5 and y = 2 + 25 · 5 = 4, so P is (5, 4).
Try a similar one
Point P divides AB in the ratio 1:2. What fraction of the way from A to B is P?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Partitioning a Directed Line Segment
A ratio m:n splits the segment into m + n equal parts, and P is m of those parts away from A. So P is mm + n of the way from A to B. On a number line: P = a + mm + n · (b - a). On the coordinate plane, do the same thing for the x-coordinates and again for the y-coordinates. Example: A(1, 2), B(11, 7), ratio 2:3. P is 25 of the way: x = 1 + 25 · 10 = 5 and y = 2 + 25 · 5 = 4, so P is (5, 4).
Try a similar one
Point P divides AB in the ratio 3:1. What fraction of the way from A to B is P?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Log in to save your progress.
Partitioning a Directed Line Segment — Easy Worksheet 1
A point P that divides AB in the ratio m:n has AP:PB = m:n, measured from A toward B. Write points as ordered pairs like (3, -2) and ratios like 2:3.