Math Problem Statement

In the given figure, if the line segment AB is intercepted by the y-axis and x-axis at C and D, respectively, such that AC: AD = 1: 4 and D is the midpoint of CB. Find the coordinates of D, C and B.

Solution

Let's solve Question 89 from the image.

Problem Breakdown:

  • We are given that line segment ABAB intersects the y-axis at CC and the x-axis at DD.
  • The coordinates of AA are (2,6)(-2, 6).
  • The ratio AC:AD=1:4AC:AD = 1:4, and DD is the midpoint of CBCB, where BB has coordinates (p,q)(p, q).

We are asked to find the coordinates of CC, DD, and BB.

Step-by-step Solution

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Ratio and Proportion
Midpoint Formula

Formulas

Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)
Section formula: (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)

Theorems

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Suitable Grade Level

Grades 9-10