Question

What are the coordinates of point B in the diagram?

(3.25, -2.5)

(4, -5)

(1, 3)

(2.5, 0)

Answer 1

Answer: The co-ordinates of point B are (4, -5).

Step-by-step explanation: We are given to find the co-ordinates of point B in the diagram.

From the diagram, we note that

the co-ordinates of point A and C are (1, 5) and (1.75, 2.5) respectively.

Also, the point C divides the line segment AB internally in the ratio 1 : 3.

We know that if a point P divides a line segment joining the points (a, b) and (c, d) internally in the ratio m : n, then the co-ordinates of the point P are

`P=\left((mc+na)/(m+n),(md+nb)/(m+n)\right).`

Here, (a, b) = (1, 5), m : n = 1 : 3 and (c, d) = ?

Therefore, the co-ordinates of point C will be

`C=\left((1* c+3*1)/(1+3),(1* d+3*5)/(1+3)\right)\\\\\\\Rightarrow (1.75,2.5)=\left((c+3)/(4),(d+15)/(4)\right)\\\\\\\Rightarrow 1.75=(c+3)/(4),~~~~~2.5=(d+15)/(4)\\\\\\\Rightarrow c+3=7,~~~~~~~~\Rightarrow d+15=10\\\\\\\Rightarrow c=4,~~~~~~~~~~~~~\Rightarrow d=-5.`

Thus, the co-ordinates of point B are (4, -5).

Answer 2

Let the cordinates of B be (x, y), then
(3(1) + x)/4 = 1.75 and (3(5) + y)/4 = 2.5
3 + x = 7 and 15 + y = 10
x = 7 - 3 and y = 10 - 15
x = 4 and y = -5

Therefore, the coordinate of B is (4, -5)