Find the missing y-coordinate that makes the two triangles congruent

1.	Find the missing y-coordinate that makes the two triangles congruent.Triangle ABC: A(8,4), B(2,6), C(5, 0)Triangle MNO: M(7,4), N(1,2), O(4, y)(1 point)−4−404−2
Answer» Option (d) is correct answer. Since, congruent triangle have equal area. Area of triangle ABC = \(\frac{1}{2}\)\(\begin{vmatrix}8 & 4 & 1 \\2 & 6 & 1 \\5 & 0 & 1\end{vmatrix}\) = \(\frac{1}{2}\) \(\big(\)8(6 - 0) - 4(2 - 5) + 1(0 - 30)\(\big)\) = \(\frac{1}{2}\) \(\big(\)48 + 12 - 30\(\big)\) = \(\frac{1}{2}\)(60 - 30) = 15 Area of triangle MNO = \(\frac{1}{2}\)\(\begin{vmatrix}7 & 4 & 1 \\1 & 2 & 1 \\4 & y & 1\end{vmatrix}\) = \(\frac{1}{2}\) \(\big(\)7(2 - y) - 4(1 - 4) + 1(y - 8)\(\big)\) = \(\frac{1}{2}\) (14 - 7y + 12 + y - 8) = \(\frac{1}{2}\)(18 - 6y) = 9 - 3y since given that triangle ABC and triangle MNO are congruent. Therefore, there are must be equal Therefore 9y - 3y = 15 \(\Rightarrow\) 3y = 9 - 15 = -6 \(\Rightarrow\) y = -2

Find the missing y-coordinate that makes the two triangles congruent.Triangle ABC: A(8,4), B(2,6), C(5, 0)Triangle MNO: M(7,4), N(1,2), O(4, y)(1 point)−4−404−2

Answer»

Option (d) is correct answer.

Since, congruent triangle have equal area.

Area of triangle ABC = \(\frac{1}{2}\)\(\begin{vmatrix}8 & 4 & 1 \\2 & 6 & 1 \\5 & 0 & 1\end{vmatrix}\)

= \(\frac{1}{2}\) \(\big(\)8(6 - 0) - 4(2 - 5) + 1(0 - 30)\(\big)\)

= \(\frac{1}{2}\) \(\big(\)48 + 12 - 30\(\big)\) = \(\frac{1}{2}\)(60 - 30) = 15

Area of triangle MNO = \(\frac{1}{2}\)\(\begin{vmatrix}7 & 4 & 1 \\1 & 2 & 1 \\4 & y & 1\end{vmatrix}\)

= \(\frac{1}{2}\) \(\big(\)7(2 - y) - 4(1 - 4) + 1(y - 8)\(\big)\)

= \(\frac{1}{2}\) (14 - 7y + 12 + y - 8)

= \(\frac{1}{2}\)(18 - 6y) = 9 - 3y

since given that triangle ABC and triangle MNO are congruent.

Therefore, there are must be equal

Therefore 9y - 3y = 15

\(\Rightarrow\) 3y = 9 - 15 = -6

\(\Rightarrow\) y = -2

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