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On the cartesian plane, $Q$ is the midpoint of the straight line $PR$ . Find the values of $x$ and $y$ .

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x = 8, y = 3

x = 4, y = 3 \frac{1}{2}

x = 3, y = 2

x = 4, y = 2

answer is B.

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Detailed Solution

Given, Q is the midpoint of PR.
Question Image

We need to find the value of x & y.
Midpoint of two point

{(x}_{1}, y_{1})

{(x}_{2}, y_{2})

is ,

(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

.
Now, P(1,4) is

{(x}_{1}, y_{1})

and R(7,y) is

{(x}_{2}, y_{2})

and the midpoint is Q(x,3).

(x, 3) = (\frac{1 + 7}{2}, \frac{4 + y}{2})

Considering x coordinates of the midpoint,

x = \frac{7 + 1}{2};

\Rightarrow x = 4

And, considering y coordinates of the midpoint,

3 = \frac{y + 4}{2}

\Rightarrow y = 2

Thus, the value of x is 4 and y is 2.
Therefore, option (2) is correct.

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