﻿ Points A(\sqrt{2},4 ) , B(6,-\sqrt{3} ) , and C are collinear. If B is the

#### Multiple Choice Question (MCQ)

Points A(\sqrt{2},4 ) , B(6,-\sqrt{3} ) , and C are collinear. If B is the midpoint of line segment AC , approximately what are the (x,y) coordinates of point C ?

1. ×

(3.71,1.13)

2. ×

(3.71,5.73)

3. ×

(7.41,-7.46)

4. (10.59, -7.46)

5. ×

(10.59, 5.73)

Collected in the board: Coordinate geometry

Steven Zheng posted 3 years ago

1. "Collinear" implies the three points lie on the same line. Two points will determine a linear equation if their coordinates are given. In this question, the coordinates of A and B are given, the linear equation for the line is determined. According to the condition B is the midpoint of line segment AC, we can use the coordinates formula for a midpoint between two points to determine the coordinates of C.

x_B = \dfrac{x_A+x}{2}
(1)
y_B = \dfrac{y_A+y}{2}
(2)

Substitute the x coordinates of A, B to (1)

\dfrac{\sqrt{2}+x }{2}=6

We get

x= 12-\sqrt{2}\approx 10.59

Substitute the y coordinates of A, B to (2)

\dfrac{4+y}{2}=-\sqrt{3}

Then we get

y = -2\sqrt{3} -4 \approx -7.46

So D is the correct solution.

Steven Zheng posted 3 years ago

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