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4 years ago

If triangle ABC is dilated by a scale factor of 2 with a dilation center of A, what will be the coordinates of point b’?

Mathematics

1 answer:

mojhsa [17]4 years ago

8 0

Answer:

In the given figure the sides of triangle measures as follows:

AB= 4 units,

BC= 6 units,

Since triangle ABC is right angled triangle, to find AC we will have to use Pythagorean theorem,

AB² + BC² = AC²

Plugging the values of AB and BC to find AC,

4² + 6² = AC²

16+36=AC²

AC = 7.48

Now if the triangle is dilated by a scale factor of 2, each side will be multiplied by 2 to get the new triangle A'B'C'

side A'B' = 2* AB = 2*4= 8 units

side B'C' = 2* BC = 2*6 =12 units

side A'C' = 2*AC = 2*7.48 = 14.96 units

Perimeter of triangle = sum of three sides

Perimeter of triangle A'B'C' = A'B' + B'C' + A'C'= 8+12 + 14.96 = 34.96 units.

Perimeter of triangle ABC = AB+BC + AC = 4+6+7.48 = 17.48 units.

Perimeter of triangle A'B'C' = 2* Perimeter of triangle ABC

The perimeter of new triangle A'B'C' is 34.96 units which is twice that of triangle ABC.

Answer : A) The perimeter of A'B'C' is 2 times the perimeter of ABC.

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3 years ago

In the right ∆ABC, the hypotenuse AB = 17 cm. M is the midpoint of the hypotenuse. Find the legs if PAMC=32 cm and PBMC=25 cm

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Answer:

The length of the legs is 8.64cm and 14.64cm respectively

Step-by-step explanation:

I've added an attachment to aid my explanation.

At different intervals, I'll be making reference to it.

Given

$AB = 17$

$PAMC = 32$

$PBMC = 25$

From the attachment, we have:

$y + z = AB$

Since, M is the Midpoint

$y = z = \½AB$

Substitute 17 for AB

$y = z = \½ * 17$

$y = z = 8.5$

Also, from the attachment

$v + x + z = PAMC$

$v + x + y = 32$

Substitute 8.5 for y

$v + x + 8.5 = 32$

$v + x = 32 - 8.5$

$v + x = 23.5$ --------- (1)

Also, from the attachment

$v + w + z = 25$

Substitute 8.5 for z

$v + w + 8.5 = 25$

$v + w = 25 - 8.5$

$v + w = 17.5$ ----------- (2)

Subtract (2) from (1)

$v - v + x - w = 23.5 - 17.5$

$x - w = 6$

Make x the subject

$x = 6 + w$

Apply Pythagoras Theorem:

We have that:

$AB^2 = AC^2 + BC^2$

The above can be replaced with

$17^2 = x^2 + w^2$ (see attachment)

$289 = x^2 + w^2$

Substitute 6 + w for x

$289 = (6 + w)^2 + w^2$

$289 = 36 + 12w + w^2 + w^2$

$289 - 36 = 12w + 2w^2$

$253 = 12w + 2w^2$

Reorder

$2w^2 + 12w - 253 = 0$

Solve using quadratic equation:

$w = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

$a = 2$

$b = 12$

$c = -253$

$w = \frac{-12 \± \sqrt{12^2 - 4 * 2 * -253}}{2 * 2}$

$w = \frac{-12 \± \sqrt{144 + 2024}}{4}$

$w = \frac{-12 \± \sqrt{2168}}{4}$

$w = \frac{-12 \± 46.56}{4}$

Split:

$w = \frac{-12 + 46.56}{4}$ or $w = \frac{-12 - 46.56}{4}$

$w = \frac{34.56}{4}$ or $w = \frac{-58.56}{4}$

$w = 8.64$ or $w = -14.64$

But length can't be negative

So:

$w = 8.64$

Recall that: $x = 6 + w$

$x = 6 + 8.64$

$x = 14.64$

<em>Hence, the length of the legs is 8.64cm and 14.64cm respectively</em>

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Read 2 more answers