9514 1404 393
Answer:
5
Step-by-step explanation:
A graph can be helpful. It shows possible integer coordinates of Z could be ...
(-1, 2) or (-5, 1)
These have distances 5 and 4√2 from Y, respectively. Of these, only the length YZ = 5 appears on your list of possible answers.
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The hypotenuse of a right triangle is the diameter of the circumcircle. That is, the right angle vertex (Z) appears on a circle whose center is the midpoint of the hypotenuse. Here, that circle center is C = (-4-1, 2-3)/2 = (-5/2, -1/2). The given point Y differs from this by C - Y = (-5/2 -(-1), -1/2 -(-3)) = (-3/2, 5/2). So, a point with integer coordinates will be 2×(5/2) = 5 units above point Y, which puts it in the 2nd quadrant.
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Adding any of the 8 combinations (±3/2, ±5/2) or (±5/2, ±3/2) to the circle center coordinates will result in integer coordinates for the right angle vertex. Of these, only the ones listed above are in the second quadrant. A couple are on the y-axis, and two of the possibilities are X and Y. The other two are in the third quadrant.
Step-by-step explanation:
Given that,
The area of an isosceles triangle, A = 192 cm²
The ratio of base and height is 3:2.
The area of a triangle is given by :
Let base = 3x and height = 2x
So,
Base = 3x = 3(8) = 24 cm
Height = 2x = 2(8) = 16 cm
Let equal sides be 16 cm and base be 24
So,
Perimeter = sum of all sides
= 16+16+24
= 56 cm
Hence, this is the required solution.
The coefficients of x and y in the first equation are 3 and -4, respectively.
The coefficients of x and y in the second equation are 1 and 6, respectively.
The coefficient matrix lists these coefficients in order on successive rows, so it will be ...