Match each step Chloe answered this question by completing the steps shown.3Find point Con AB that is - of the distance from A to B. The coordinates of A are (2, 4). The coordinates of B are (6,8).What are the coordinates of C?Match each step of Chloe's solution to its appropriate justification.B-(x, +(-x). y +0: - y)B = (x+-x). yı +-)B =4B = (2 + 3, 4 +3)B = (5,7)Justification BankSimplifySection FormulaMidpoint FormulaCongruent SegmentsFractional Distance FormulaTerminal EndpointSubstitute a = 3 and b = 4( = (2, 4), (r. v) = (6,8)SimplitySubstitute a = 4 and b = 3(x))= (2,6). C v) = (4)Combine Like Terms

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Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Match each step

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Step 1

Given information:

The point C lies on AB that divides the line into the ratio $\frac{3}{4}$ . The coordinates of $A are (2, 4) and B are (6, 8)$ .

Calculation:

We have to find the coordinate C.

$\begin{array}{rcl} C & = & (x_{1} + \frac{a}{b} (x_{2} - x_{1}), y_{1} + \frac{a}{b} (y_{2} - y_{1})) section formula \\ = & (x_{1} + \frac{3}{4} (x_{2} - x_{1}), y_{1} + \frac{3}{4} (y_{2} - y_{1})) Substitute a = 3 and b = 4 \\ = & (2 + \frac{3}{4} (6 - 2), 4 + \frac{3}{4} (8 - 4)) Substitute (x_{1}, y_{1}) = (2, 4) and (x_{1}, y_{1}) = (2, 4) \end{array}$

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