Question

the coordinates of three vertices of parallelogram abcd are a(-1,0), b(4,0), and c(5,4). what are the coordinates of vertex d

Answer 1

(0,4) you find the slope for AB , slope for AB is = DC

Answer 2

Answer: The required co-ordinates of vertex D are (0, 4).

Step-by-step explanation: Given that the co-ordinates of three vertices of a parallelogram ABCD are A(-1,0), B(4,0) and C(5,4).

We are to find the co-ordinates of vertex D.

Let (a, b) be the co-ordinates of the vertex D.

Since the opposite sides of a parallelogram are parallel to each other and the slopes of two parallel lines are equal, so we must have

`\textup{slope of AB}=\textup{slope of CD}\\\\\\\Rightarrow (0-0)/(4-(-1))=(b-4)/(a-5)\\\\\\\Rightarrow (0)/(5)=(b-4)/(a-5)\\\\\\\Rightarrow 0=(b-4)/(a-5)\\\\\Rightarrow b-4=0\\\\\Rightarrow b=4`

and

`\textup{slope of BC}=\textup{slope of AD}\\\\\\\Rightarrow (4-0)/(5-4)=(b-0)/(a-(-1))\\\\\\\Rightarrow (4)/(1)=(b)/(a+1)\\\\\\\Rightarrow 4=(4)/(a+1)\\\\\\\Rightarrow 1=(1)/(a+1)\\\\\Rightarrow a+1=1\\\\\Rightarrow a=1-1\\\\\Rightarrow a=0.`

Thus, the required co-ordinates of vertex D are (0, 4).