Question

8 If A (2,-5), B(-2, 1) and C (4,9) are the vertices of triangle ABC and BD is then median then co-ordinates of D are​

Answer 1

Solution:

➛ Let A = ( 2, -5 )

➛ Let B = ( -2, 1 )

➛ Let C = ( 4, 9 )

When we join A, B, C points they make a triangle and they are the vertices of triangle ABC.

Steps:

• On a graph, draw the co-ordinate axes x0x' and y0y' intersecting at origin 0.

• With proper scale, mark the numbers on the two co-ordinate axis.

For plotting any point two steps are to be adopted:

• Starting from the origin 0 moves 2 unit along the positive side of the x-axis i.e, to the left of the origin 0.
• Now from here move 5 units that is parallel a negative direction of y-axis.
• Place a dot at the point reached.
• Label this as A ( 2, -5 ).

➤ Similarly plot the other points B ( -2, 1 ) and C ( 4, 9 )

Now,

We know that BD is the median of AC.

Coordinates of A = ( 2, -5 ) and C = ( 4, 9 )

⟹ Coordinates of D = ( (x₂ + x₁)/2, (y₂ + y₁)/2 )

Here,

• x₁ = 2
• x₂ = 4
• y₁ = -5
• y₂ = 9

Putting the values,

⟹ Coordinates of D = ( (4 + 2)/2, (9 + -5)/2 )

⟹ Coordinates of D = ( 6/2, 4/2 )

⟹ Coordinates of D = ( 3, 2 )

∴ Coordinates of D are ( 3, 2 ).

Refer the attachment ✔

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