Math Problem Statement

The coordinates of the vertices of the triangle shown are P(2, 13), Q(7, 1), and R(2, 1). What is the length of segment PQ in units?

Solution

To solve for the length of segment PQPQ in the triangle, we will use the distance formula:

d=(x2x1)2+(y2y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

For points P(2,13)P(2, 13) and Q(7,1)Q(7, 1):

  • x1=2x_1 = 2, y1=13y_1 = 13
  • x2=7x_2 = 7, y2=1y_2 = 1

Substitute into the formula:

d=(72)2+(113)2d = \sqrt{(7 - 2)^2 + (1 - 13)^2} d=52+(12)2d = \sqrt{5^2 + (-12)^2} d=25+144d = \sqrt{25 + 144} d=169d = \sqrt{169} d=13unitsd = 13 \, \text{units}

So, the length of segment PQPQ is 1313 units. The correct answer is D. 13 units.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

  1. How do you calculate the distance between two points on a coordinate plane?
  2. What is the formula for finding the length of a diagonal line segment?
  3. How can you verify if three points form a right triangle?
  4. What would the length of segment PRPR be using the same formula?
  5. How do the coordinates of points affect the orientation of a triangle on a graph?

Tip: The distance formula is derived from the Pythagorean theorem, where the line segment between two points acts as the hypotenuse of a right triangle.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Distance Formula

Formulas

Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Theorems

Pythagorean theorem

Suitable Grade Level

Grades 8-10