Class 9th Maths Ganita Manjari - Part I Chapter 1: Orienting Yourself: The Use of Coordinates Exercise 3: End-Of-Chapter Exercises Question 10 Solution

Question

Use the connection you found to find the coordinates of B given that M (-7, 1) is the midpoint of A (3, -4) and B (x, y).

Accepted Answer

Find the x-coordinate of B using the midpoint relationship.

**Note:** The midpoint of ($x_1, y_1$) and ($x_2, y_2$) is: (\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2})
 $\dfrac{3 + x}{2}$ = -7 $\quad$ ${color:#625b5f}	extit{[x1 = 3, x2 = x, and midpoint x-coordinate = -7]}{/color}$|||	ext{\Rightarrow 3 + x = -7 	imes 2 = -14}|||	ext{\Rightarrow x = -14 - 3 = -17} Find the y-coordinate of B using the midpoint relationship.
 $\dfrac{-4 + y}{2} = 1$ $\quad$ ${color:#625b5f}	extit{[y1 = -4, y2 = y, and midpoint y-coordinate = 1]}{/color}$|||	ext{\Rightarrow -4 + y = 1 	imes 2 = 2}|||	ext{\Rightarrow y = 2 + 4 = 6} Use the x- and y-coordinates found in the previous steps to write the coordinates of B.
 {green}	extbf{Answer: B = (-17, 6)}{/green}

Question: 10

Answer