GMAT: Math 54 | Problem solving | GMAT | Khan Academy

TL;DR

This video discusses how to construct right triangles on the XY plane and determine the number of possible triangles that satisfy given conditions.

Transcript

We're on problem 248, truly the home stretch. Right triangle pqr is to be constructed on the xy plane. Let me draw an xy plane, that seems like it should be useful. So that's x, and y -- I'm sorry, that's y and that's x. Let me label them since I said them wrong. y and x, that should be second nature to you at this point. If you start the xy plane ... Read More

Key Insights

• #️⃣ The total number of possible triangles is determined by multiplying the number of options for each vertex.
• 👉 The x-coordinate of point P can take on 10 values, the y-coordinate of point P can take on 11 values, and the x-coordinate of point R can take on 9 values.
• 😀 The y-coordinate of point Q can take on any of the remaining 10 values.
• ☺️ The total number of possible triangles satisfying the given conditions is 110 x 9 x 10 = 9900.

Questions & Answers

Q: How many different possible x-coordinates can the point P have?

The point P can have 10 different x-coordinates, ranging from -4 to 5.

Q: What are the boundaries for the y-coordinate of the point P?

The y-coordinate of point P is between 6 and 16, including both endpoints, resulting in 11 possible values.

Q: How many valid locations are there for point R on the x-axis?

There are 9 potential x-coordinates for point R, as one x-coordinate is already occupied by point P.

Q: How many different y-coordinates can the point Q have?

Point Q can have any of the remaining 10 y-coordinates, as one y-coordinate is occupied by point P and cannot be duplicated.

Summary & Key Takeaways

• The video explains how to construct a right triangle on the XY plane, given specific conditions for the x and y coordinates of its vertices.

• The video breaks down the process of determining the number of different possible triangles that can be constructed based on the given conditions.

• It demonstrates how to calculate the total number of valid triangles by considering the number of potential options for each vertex.