Mathematics: Con Triangle ABC with vertices A(0,0), B(0,4), and C(3,0) is dilated to form triangle ADE. What is the E if D has coordinates (0,6)? 106

Con Triangle ABC with vertices A(0,0), B(0,4), and

Ответ:

sadiejane1125

13.07.2021

The coordinates of E are $E(x,y) = \left(\frac{9}{2}, 0 \right)$ .

Step-by-step explanation:

The triangle ABC represents a right triangle as both sides AB and AC are orthogonal to each other. The side AB is in the y axis, whereas the side AC is in the x axis. The triangle is dilated with respect to the origin, in which point A is set.

Vectorially speaking, dilation is defined by the following operation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y) - O(x,y)]$ (1)

Where:

O(x,y) - Point of reference.

P(x,y) - Original point.

P'(x,y) - Dilated point.

- Dilation factor.

By applying this operation, point B becomes point D:

B(x,y) = (0,4) , D(x,y) = (0,6)

$D(x,y) = (0,0) + k\cdot [(0,4)- (0,0)]$

$D(x,y) = (0,0) + k\cdot (0,4)$

$(0,6) = (0,0) +(0,4\cdot k)$

$(0, 6) = (0,4\cdot k)$

$k = \frac{3}{2}$

Lastly, we transform point C into point E by applying the same operation: C(x,y) = (3, 0) , O(x,y) = (0,0) and $k = \frac{3}{2}$

$E(x,y) = (0,0) + \frac{3}{2}\cdot [(3,0)-(0,0)]$

$E(x,y) = \left(\frac{9}{2}, 0 \right)$

The coordinates of E are $E(x,y) = \left(\frac{9}{2}, 0 \right)$ .

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Con Triangle ABC with vertices A(0,0),
B(0,4), and C(3,0) is dilated to
form triangle ADE. What is the
E if D has coordinates
(0,6)?
106

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