Middle School

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The coordinates of the vertices of ΔMDT are M(4, −3), D(−6, −1), and T(7, −8). Identify the perimeter of ΔMDT. Round each side length to the nearest tenth before adding.

A. 32.4
B. 36.9
C. 30.8
D. 29.1

Answer :

[tex]M=(4,-3)\qquad D=(-6,-1)\qquad T=(7,-8)\\\\\\
|MD|=\sqrt{\big(-6-4\big)^2+\big(-1-(-3)\big)^2}=\sqrt{\big(-10\big)^2+\big(-1+3\big)^2}=\\\\=\sqrt{100+2^2}=\sqrt{104}\approx\boxed{10.2}\\\\\\\\
|DT|=\sqrt{\big(7-(-6)\big)^2+\big(-8-(-1)\big)^2}=\sqrt{\big(7+6\big)^2+\big(-8+1\big)^2}=\\\\=\sqrt{13^2+(-7)^2}=\sqrt{169+49}=\sqrt{218}\approx\boxed{14.8}\\\\[/tex]


[tex]|TM|=\sqrt{\big(4-7\big)^2+\big(-3-(-8)\big)^2}=\sqrt{\big(-3\big)^2+\big(-3+8\big)^2}=\\\\=\sqrt{9+5^2}=\sqrt{9+25}=\sqrt{34}\approx\boxed{5.8}[/tex]

So the perimeter:

[tex]P_{\Delta MDT}=|MD|+|DT|+|TM|\approx10.2+14.8+5.8=\boxed{30.8}[/tex]

Answer C.

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