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densk [106]
3 years ago
10

Pentagon PQRST and its reflection, pentagon P'Q'R'S'T', are shown in the coordinate plane below.

Mathematics
1 answer:
Step2247 [10]3 years ago
5 0
<span>draw a straight line through those points. that's your line of reflection. now you have only to figure out which of those equations corresponds to it.
So it y=x</span>
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Determine the ratio in which the point (–6, m) divides the join of A(–3, –1) and B(–8, 9). Also, find the value of m.
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Answer:

Ratio = 3 : 2 and value of m = 5.

Step-by-step explanation:

We are given the end points ( -3,-1 ) and ( -8,9 ) of a line and a point P = ( -6,m ) divides this line in a particular ratio.

Let us assume that it cuts the line in k : 1 ratio.

Then, the co-ordinates of P = ( \frac{-8k-3}{k+1},\frac{9k-1}{k+1} ).

But, \frac{-8k-3}{k+1} = -6

i.e. -8k-3 = -6k-6

i.e. -2k = -3

i.e. k = \frac{3}{2}

So, the ratio is k : 1 i.e \frac{3}{2} : 1 i.e. 3 : 2.

Hence, the ratio in which P divides the line is 3 : 2.

Also, \frac{9k-1}{k+1} = m where k = \frac{3}{2}

i.e. m = \frac{\frac{9 \times 3}{2}-1}{\frac{3}{2}-1}

i.e. m = \frac{27-2}{3+2}

i.e. m = \frac{25}{5}

i.e. m = 5.

Hence, the value of m is 5.

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