Question

In a coordinate plane, if points C(2, 5), D(- 1, 2) and E(x, y) lie on line 4, which of the following would be the coordinate of point E?A. (0, 1)B. (1,1)C. (0, 2)D, (1, 4)

Answer 1

To answer this, we will find the equation of the line that passes through point C and D and check which option is in the same line, this will be the answer.

First, let's find the slope using th coordinates of the points C and D:

`s=(y_D-y_C)/(x_D-x_C)=(2-5)/(-1-2)=(-3)/(-3)=1`

Now, we can use point C, for example, to right in the slope-point form:

`\begin{gathered} (y-y_C)=s(x-x_C) \\ y-5=1(x-2) \\ y=x-2+5 \\ y=x+3 \end{gathered}`

With this equation, we can input values of x and check is we get the same y.

Alternative A and C have x = 0, so let's check it:

`\begin{gathered} y=x+3 \\ y=0+3 \\ y=3 \end{gathered}`

I got y = 3, neither alternative have y = 3, so it isn't A nor C.

B and D have x = 1, let's check it:

`\begin{gathered} y=x+3 \\ y=1+3 \\ y=4 \end{gathered}`

We got y = 4, which matches alternative D.

So, the correct alternative is D.