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r-ruslan [8.4K]
3 years ago
10

Find the coordinates of the orthocenter for XYZ with X(-5,-1) Y(-2,4), Z(3,-1)

Mathematics
1 answer:
V125BC [204]3 years ago
4 0

9514 1404 393

Answer:

  (-2, 2)

Step-by-step explanation:

The orthocenter is the intersection of the altitudes. The altitude lines are not difficult to find here. Each is a line through the vertex that is perpendicular to the opposite side.

Side XZ is horizontal, so the altitude to that side is the vertical line through Y. The x-coordinate of Y is -2, so that altitude has equation ...

  x = -2

__

Side YZ has a rise/run of -1/1 = -1, so the altitude to that side will be the line through X with a slope of -1/(-1) = 1. In point-slope form, the equation is ...

  y -(-1) +(1)(x -(-5))

  y = x +4 . . . . . . . . subtract 1 and simplify

The orthocenter is the point that satisfies both these equations. Using the first equation to substitute for x in the second, we have ...

  y = (-2) +4 = 2

The orthocenter is (x, y) = (-2, 2).

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Answer:

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Step-by-step explanation:

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3 years ago
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Liam explains that drawing a yellow card is equivalent to drawing a blue card followed by a red card how many spaces forward or
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Complete question :

designs a board game in which a card is drawn on each turn. • A blue card means move forward 4 squares. • A red card means move back 6 squares. Liam suggests adding some other cards to Sia's game Part A Liam explains that drawing a yellow card is equivalent to drawing a blue card followed by a red card. How many spaces forward or backward does a player move after drawing a yellow card? Justify your answer.

Answer:

2 squares backward

Step-by-step explanation:

Given the rule :

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3 years ago
Add 5/8 inch, 11/16 inch, and 27/32 inch.
noname [10]
Hi,

Work:

Equation;

\frac{5}{8} + \frac{11}{16} + \frac{27}{32}

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\frac{5 + 11 + 27}{32}

Calculate the sum of positive numbers.

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2 \frac{5}{32}

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2.15625

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