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 intersects the y-axis at and the x-axis at .
- The coordinates of are .
- The ratio , and is the midpoint of , where has coordinates .
We are asked to find the coordinates of , , and .
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
-
Suitable Grade Level
Grades 9-10
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