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Scrat [10]
3 years ago
5

The endpoints of line RS are R(1, -3) and S(4,2). Find RS

Mathematics
1 answer:
laila [671]3 years ago
7 0

Answer:

Part 1) RS=\sqrt{34}\ units

Part 2) CD=\sqrt{125}\ units

Part 3) The coordinates of endpoint C are (13,5)

Step-by-step explanation:

Part 1) The endpoints of line RS are R(1, -3) and S(4,2). Find RS

we now that

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

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

substitute the values

RS=\sqrt{(2+3)^{2}+(4-1)^{2}}

RS=\sqrt{(5)^{2}+(3)^{2}}

RS=\sqrt{34}\ units

Part 2) The endpoints of line CD are C(-8,-1) and D(2,4). Find CD

we now that

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

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

substitute the values

CD=\sqrt{(4+1)^{2}+(2+8)^{2}}

CD=\sqrt{(5)^{2}+(10)^{2}}

CD=\sqrt{125}\ units

Part 3) The midpoint of line AC is M(5,6). One endpoint is A(-3,7). Find the coordinates of endpoint C

The formula to calculate the midpoint between two points is equal to

M=(\frac{x1+x2}{2},\frac{y1+y2}{2})

Let

(x2,y2)-------> the coordinates of point C

(x1,y1) -------> the coordinates of point A

substitute the given values

(5,6)=(\frac{-3+x2}{2},\frac{7+y2}{2})

write the equations

\frac{-3+x2}{2}=5\\ \\-3+x2=10\\ \\ x2=10+3\\ \\x2=13

\frac{7+y2}{2}=6\\\\ 7+y2=12\\ \\ y2=12-7\\ \\y2=5

therefore

The coordinates of endpoint C are (13,5)

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