Nathan is drawing a square LMNO on a coordinate grid. He plotted three points at L (3, -4), M (3, 7), and N (14, 7). Where should he plot point O to make the square?
Answer
(14, -4)
(-14, 4)
(-14, -18)
(14, 18)
Points P (-6, 4), Q (-4, 4), R (-4, 2), and S (-6, 2) are plotted on a coordinate grid. Which statement is correct about the points?
Answer
They form a square because PR is perpendicular to RS.
They form a square because diagonals PR and QS are congruent.
They do not form a square because the opposite sides are not parallel.
They do not form a square because the sides of quadrilateral PQRS are not congruent.
When an altitude is drawn to the hypotenuse of a right triangle, the lengths of the segments of the hypotenuse are 4 and 9. What is the length of the altitude?
Answer
4
6
9
13
Two end points of a line segment are (-12, -2) and (-6, -10). What are the coordinates of the point on the line through which its bisector passes?
Answer
(-18, -12)
(-11, -4)
(-9, -6)
(-7, -8)
Answer
(14, -4)
(-14, 4)
(-14, -18)
(14, 18)
Points P (-6, 4), Q (-4, 4), R (-4, 2), and S (-6, 2) are plotted on a coordinate grid. Which statement is correct about the points?
Answer
They form a square because PR is perpendicular to RS.
They form a square because diagonals PR and QS are congruent.
They do not form a square because the opposite sides are not parallel.
They do not form a square because the sides of quadrilateral PQRS are not congruent.
When an altitude is drawn to the hypotenuse of a right triangle, the lengths of the segments of the hypotenuse are 4 and 9. What is the length of the altitude?
Answer
4
6
9
13
Two end points of a line segment are (-12, -2) and (-6, -10). What are the coordinates of the point on the line through which its bisector passes?
Answer
(-18, -12)
(-11, -4)
(-9, -6)
(-7, -8)
-
For future reference, if you have more than one question, please post them one at a time as separate questions online. When you have questions like this squeezed into one, people may not want to help you beause it seems like it is too much to ask all at one time.
In order to find where point O is going to be drawn, you have to look at where every all the other points are located. Since L and M are 7 - (-4) = 11 spaces apart, this means that LM is 11 units long. The point N is to the right of M, which means O must be below it, to the right of L.
If it is to the right of L(3, -4), this means you have to add 11 to L's x-coordinate, (3 + 11, -4),
which is (14, -4).
For the next one, you have P (-6, 4), Q (-4, 4), R (-4, 2), and S (-6, 2). PQ's length is 2, QR's length is 2 and RS's length is 2. This would imply (if you quickly sketched it), that PS is also 2. So the sides are ALL equal and you can obviously see that they are all right angles, so it is a square because of those reasons.
If the hypotenuse's segments are 4 and 9, this means the hypotenuse is 13. Knowing your Pythagorean triples, you automatically have 5-12-13 triangle. This means, again if you quickly sketch the triangle with its altitude, then you have the triangle broken into two smaller ones.
Now we want to find the altitude, which means since we already know two of the sides of the smaller triangles, we can use Pythagoren Theorem to find it.
Let's use the smaller triangle:
x^2 + 4^2 = 5^2
x^2 + 16 = 25
x^2 = 9
x = 3
The altitude is 3.
The last one, just use the Midpoint formula:
((x1 + x2)/2, (y1+y2)/2)
((-12 + -6)/2, (-2 + -10)/2)
(-18/2 , -12/2)
(-9, -6) is where your midpoint is going to be.
Hope this helps.
In order to find where point O is going to be drawn, you have to look at where every all the other points are located. Since L and M are 7 - (-4) = 11 spaces apart, this means that LM is 11 units long. The point N is to the right of M, which means O must be below it, to the right of L.
If it is to the right of L(3, -4), this means you have to add 11 to L's x-coordinate, (3 + 11, -4),
which is (14, -4).
For the next one, you have P (-6, 4), Q (-4, 4), R (-4, 2), and S (-6, 2). PQ's length is 2, QR's length is 2 and RS's length is 2. This would imply (if you quickly sketched it), that PS is also 2. So the sides are ALL equal and you can obviously see that they are all right angles, so it is a square because of those reasons.
If the hypotenuse's segments are 4 and 9, this means the hypotenuse is 13. Knowing your Pythagorean triples, you automatically have 5-12-13 triangle. This means, again if you quickly sketch the triangle with its altitude, then you have the triangle broken into two smaller ones.
Now we want to find the altitude, which means since we already know two of the sides of the smaller triangles, we can use Pythagoren Theorem to find it.
Let's use the smaller triangle:
x^2 + 4^2 = 5^2
x^2 + 16 = 25
x^2 = 9
x = 3
The altitude is 3.
The last one, just use the Midpoint formula:
((x1 + x2)/2, (y1+y2)/2)
((-12 + -6)/2, (-2 + -10)/2)
(-18/2 , -12/2)
(-9, -6) is where your midpoint is going to be.
Hope this helps.