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Umnica [9.8K]
3 years ago
6

Three collinear points on the coordinate plane are r(x,y), s(x+8h, y+8k), and p (x+6h, y+6k)

Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
5 0

Answer:

A.\frac{RP}{SP}=3

B.\frac{RP}{RS}=\frac{3}{4}

Step-by-step explanation:

<u><em>The complete question is</em></u>

Three collinear points on the coordinate plane are R(x, y), S(x+8h, y+8k), and P(x+6h, y+6k).

<em>Part A: Determine the value of RP/SP</em>

<em>Part B: Determine the value of RP/RS</em>

we know that

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

R(x,y),S(x+8h,y+8k) and P(x+6h,y+6k)

Part A.We have to find the value of \frac{RP}{SP}

step 1

Find the distance RP

R(x,y),P(x+6h,y+6k)

substitute the values in the formula

RP=\sqrt{(x+6h-x)^2+(y+6k-y)^2}

RP=\sqrt{36h^2+36 k^2}

RP=6\sqrt{h^2+k^2}

step 2

Find the distance SP

S(x+8h,y+8k),P(x+6h,y+6k)

substitute the values in the formula

SP=\sqrt{(x+6h-x-8h)^2+(y+6k-y-8k)^2}

SP=\sqrt{4h^2+4k^2}

SP=\sqrt{4(h^2+k^2)}

SP=2\sqrt{h^2+k^2}

step 3

<em>Find the ratio  RP/SP</em>

\frac{RP}{SP}=\frac{6\sqrt{h^2+k^2}}{2\sqrt{h^2+k^2}}

\frac{RP}{SP}=3

Part B. We have to determine the value of \frac{RP}{RS}

step 1

Find the distance RS

R(x,y),S(x+8h,y+8k)

RS=\sqrt{(x+8h-x)^2+(y+8k-y)^2}

RS=\sqrt{64h^2+64k^2}

RS=\sqrt{64(h^2+k^2)}

RS=8\sqrt{h^2+k^2}

step 2

<em>Find the ratio RP/RS</em>

\frac{RP}{RS}=\frac{6\sqrt{h^2+k^2}}{8\sqrt{h^2+k^2}}

\frac{RP}{RS}=\frac{3}{4}

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