Algebraic midpoint of a segment exercise | Geometry | 8th grade | Khan Academy

TL;DR

Given the midpoint of segment JL, we can find the lengths of JK, KL, and JL using algebraic equations and properties of midpoints.

Transcript

We're told that K is the midpoint of segment, JL. So that tells us that segment JK is going to be congruent to segment KL, that they're going to be the exact same length. And they tell us that segment JK is equal to 8x minus 8. So this distance right over here is equal to 8x minus 8. And then they tell us that segment KL is equal to 7x minus 6, tha... Read More

Key Insights

• 🗂️ The midpoint of a segment divides it into two congruent segments.
• 😑 The lengths of segments can be determined by setting expressions for their lengths equal to each other.
• ❓ Algebra can be used to solve for variables in geometric problems.
• 😑 By substituting values into algebraic expressions, we can find the lengths of segments.
• ✅ Checking our solutions using different approaches helps ensure the validity of our calculations.
• ➗ Midpoints are important in determining congruence and division of segments.
• ❓ Algebraic equations can represent geometric properties and relationships.

Questions & Answers

Q: How do we know that JK and KL are congruent?

We are told that K is the midpoint of JL. This means that JK and KL must be equal in length since they are divided by the midpoint, making them congruent.

Q: How can we find the value of x?

We can set the expressions for JK and KL equal to each other since they are equal in length. By simplifying and solving the resulting equation, we find that x equals 2.

Q: What is the length of segment JK?

By substituting x = 2 into the expression 8x - 8, we find that JK has a length of 8 units.

Q: How can we determine the length of JL?

Since K is the midpoint, JL is equal to the sum of JK and KL. Therefore, JL has a length of 16 units.

Summary & Key Takeaways

• Given that K is the midpoint of JL, segment JK is congruent to segment KL.

• The length of segment JK is equal to 8x - 8, and the length of segment KL is equal to 7x - 6.

• By setting the two expressions equal to each other and solving for x, we find that x = 2.

• Using this value of x, we can determine that JK has a length of 8 units, KL has a length of 8 units, and JL has a total length of 16 units.