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OLga [1]
3 years ago
5

AB has coordinates A(-5,9) and B(7,- 7). Points P, Q, and I are collinear

Mathematics
1 answer:
VMariaS [17]3 years ago
6 0

Answer:

\overline{QT}

Step-by-step explanation:

We want to find the coordinates of a certain point C(x,y) such that C divides A(x_1,y_1) and B(x_2,y_2) in the ratio m:n=3:2

The x-coordinate is given by:

x=\frac{mx_2+nx_1}{m+n}

The y-coordinate is given by:

y=\frac{my_2+ny_1}{m+n}

AB has coordinates A(-5,9) and B(7,- 7)

We substitute the values to get:

x=\frac{3*7+2*-5}{3+2}

x=\frac{21-10}{5}

x=\frac{11}{5}

and

y=\frac{3*-7+2*9}{3+2}

y=\frac{-21+18}{5}

y=-\frac{3}{5}

Therefore C has coordinates  (\frac{11}{5},-\frac{3}{5})

The line segment that contains C is \overline{QT}

See attachment.

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photoshop1234 [79]
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Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.

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the converse, inverse and contrapositive of p⇒q are defined as follows:

converse: q⇒p
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contrapositive: ¬q⇒¬p

Converse of our statement:

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Inverse of the statement:

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