Question

Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W

Answer 1

The coordinates of the vertex W are (5 , -1)

Step-by-step explanation:

In the parallelogram, the diagonal bisect each other

To find a missing vertex in a parallelogram do that:

• Find the mid-point of a diagonal whose endpoints are given
• Use this mid-point to find the missing vertex
• The mid point rule is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

∵ WXYZ is a parallelogram

∴ Its diagonals are WY and XZ

∵ The diagonal bisect each other

- That mean they have the same mid-point

∴ They intersect each other at their mid-point

∵ x = (-2 , -3) and z = (7 , 7)

∴ $x_{1}$ = -2 and $x_{2}$ = 7

∴ $y_{1}$ = -3 and $y_{2}$ = 7

- Substitute them in the rule of the mid point to find the

   mid-point of XZ

∴ $M_{XZ}=(\frac{-2+7}{2},\frac{-3+7}{2})=(2.5 , 2)$

∴ The mid-point of diagonals WY and XZ is (2.5 , 2)

Let us use it to find the coordinates of vertex W

∵ W = (x , y) and Y = (0 , 5)

∴ $x_{1}$ = x and $x_{2}$ = 0

∴ $y_{1}$ = y and $y_{2}$ = 5

- Equate 2.5 by the rule of the x-coordinate of the mid-point

∵ $2.5=\frac{x+0}{2}$

- Multiply both sides by 2

∴ 5 = x + 0

∴ 5 = x

∴ The x-coordinate of point W is 5

- Equate 2 by the rule of the y-coordinate of the mid-point

∵ $2=\frac{y+5}{2}$

- Multiply both sides by 2

∴ 4 = y + 5

- Subtract 5 from both sides

∴ -1 = y

∴ The y-coordinate of point W is -1

The coordinates of the vertex W are (5 , -1)

Learn more:

You can learn more about the mid-point in brainly.com/question/10480770

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