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salantis [7]
2 years ago
12

A dilation with a scale factor of 3. 5 and centered at the origin is applied to PQ¯¯¯¯¯ with endpoints P(2, 5) and Q(2, 1)

Mathematics
1 answer:
velikii [3]2 years ago
7 0

Answer: The answer is P'(7, 17.5) and Q'(7, 3.5).

Step-by-step explanation:  Given that a line segment PQ is dilated with a scale factor of 3.5 where origin is the centre of dilation.

The end points of segment PQ are P(2, 5) and Q(2, 1).

Therefore, after dilation, the coordinates of the end points become

Thus, the coordinates of P' are (7, 17.5) and the co-ordinates of Q' are (7, 3.5).

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3 years ago
A triangle has vertices at A(-2,3), B(2,-2), and C(-2,-2). What is the area of the triangle?
Softa [21]

Answer:

The area of the given triangle ABC is 10 units.

Step-by-step explanation:

we have the area of the triangle when points are given is given by the relation

Area of triangle=

\frac{1}{2} {x1 \times (y2 - y3) + x2 \times (y3 - y1) + x3 \times (y1 - y2)}

and hence putting the Value

triangle = 1/2*( -2*(-2+2)+2*(-2-3)+(-2)*(3+2))

= 1/2*(0+2*(-5)+(-2)*5)

= 1/2*(-10-10)

= 1/2*(-20)

= (-10) units

Since area of the triangle is always positive, we neglect the minus sign and take 10 units as its area.

6 0
3 years ago
Find three consecutive natural numbers if the square of the smallest number is 65 less than the product of the remaining two num
Vedmedyk [2.9K]

Answer:

21, 22, and 23

Step-by-step explanation:

Three consecutive natural numbers can be represented as n, n+1, and n+2.

The square of the smallest number would be n^2 and its equal to the product of the other two (n+1)(n+2).

So the equation is n^2 = (n+1)(n+2) -65\\n^2 = n^2 +n+2n+2-65\\n^2=n^2+3n-63\\0=3n-63\\63=3n\\ 21=n.

If n is 21 then the next numbers are 22 and 23.

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3 years ago
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