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3 years ago

If (x-2)(y-1)=3 and (x+2)(2y-5)=15,

Mathematics

1 answer:

daser333 [38]3 years ago

5 0

Answer:

Equation 1, Multiplied by 2: 2x + 4y = 10

Equation 1, Multiplied by 2: 2x + 4y - 10 = 10 - 10

Equation 1, Multiplied by 2: 2x + 4y - 10 = 0

Equation 1, Multiplied by 2: 2x - 2x + 4y - 10 = 0 - 2x

Equation 1, Multiplied by 2: 4y - 10 = - 2x

Equation 1, Multiplied by 2: - 10 + 4y = - 2x

Notice that Equation 1 = Equation 2

One Solution

Equation 1: x - y = -10

Equation 2: 2x + 3y = 15

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nalin [4]

Answer:

A) The coordinates of the fourth vertex are:

1) x-coordinate:

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2) y-coordinate:

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Step-by-step explanation:

We need to remember that the diagonals of a parallelogram intersect each other at a half-way point and the midpoint of each diagonal is the same.

The midpoint formula is:

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Since:

$M_{AC}=M_{BD}$

We can find the coordinates of the fourth vertex $D(x,y)$ through these procedure:

1) x-coordinate:

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2) y-coordinate:

$\frac{0+2}{2}=\frac{3+y}{2}\\\\1(2)-3=y\\\\y=-1$

Therefore, fourth vertex is $D(2,-1)$

Since the point of intersection of the diagonals is the midpoint of a diagonal (Remember that $M_{AC}=M_{BD}$ ), this is:

$M_{AC}=M_{BD}=(\frac{1+3}{2},\frac{0+2}{2})\\\\M_{AC}=M_{BD}=(2,1)$

Therefore, the point of intersection of the diagonals is $(2,1)$

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