Question

The midpoint of the line joining (-a , 2b) and (-3a ,-4b) is
1 point
A.(2a,3b)
B.(-2a,-b)
C.(2a,b)
D.(-2a,-3b)​

Answer 1

Answer:

option no B) is correct answer

Step-by-step explanation:

by using mid point theorem.

Answer 2

The mid-point of the line joining the points; (-a,2b) and (-3a,-4b) is (-2a,-b).

Option B is correct.

Given:

• Two points; (-a,2b) and (-3a,-4b).

To find:

• The mid point of the line joining the points
• A.(2a,3b)
• B.(-2a,-b)
• C.(2a,b)
• D.(-2a,-3b)

Solution:

Concept/formula to be used:

If two points $A(x_1,y_1)$ and $B(x_2,y_2)$.

The mid-point C(x,y) is given by

$\bf x = \frac{x_1 + x_2}{2}$

$\bf y = \frac{y_1 + y_2}{2}$

Step 1:

Let the points are A(-a,2b) and B(-3a,-4b).

on comparison

$x_1 = - a,\: x_2 = - 3a \\ y_1 = 2b, \: y_2 = - 4b$

Step 2:

Find the mid-point.

Put the values in the formula.

$x = \frac{ - a + ( - 3a)}{2}$

$x = \frac{ - 4a}{2}$

$\bf x = - 2a$

$y = \frac{2b + ( - 4b)}{2}$

$y = \frac{ - 2b}{2}$

$\bf y = - b$

Thus,

The mid-point of the line joining the points is (-2a,-b).

Option B is correct.

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