Math Problem Statement

Write CD in component form, with C(2, -4) and D(1, -3).

Solution

To find the vector CD\overrightarrow{CD} in component form, we need to use the coordinates of points CC and DD.

Given:

  • C(2,4)C(2, -4)
  • D(1,3)D(1, -3)

The component form of a vector CD\overrightarrow{CD} is calculated by subtracting the coordinates of CC from the coordinates of DD:

CD=DxCx,DyCy\overrightarrow{CD} = \langle D_x - C_x, D_y - C_y \rangle

Where DxD_x and DyD_y are the x and y coordinates of point DD, and CxC_x and CyC_y are the x and y coordinates of point CC.

Substitute the given values:

CD=12,3(4)=1,1\overrightarrow{CD} = \langle 1 - 2, -3 - (-4) \rangle = \langle -1, 1 \rangle

So, the component form of CD\overrightarrow{CD} is 1,1\langle -1, 1 \rangle.

Let me know if you need further details or clarification! Here are some related questions you might find interesting:

  1. How do you find the magnitude of a vector?
  2. How do you represent a vector in 3D space?
  3. What is the concept of vector direction and how is it different from its magnitude?
  4. How do you add or subtract vectors in component form?
  5. How do you perform scalar multiplication on a vector?

Tip: Always double-check your subtraction of coordinates to ensure accurate component vectors!

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Math Problem Analysis

Mathematical Concepts

Vectors
Coordinate Geometry

Formulas

Vector Component Form: ⟨Dx - Cx, Dy - Cy⟩

Theorems

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Suitable Grade Level

Grades 9-10