Which of the following points has a distance of 3 from the point (−7, 4)?
(10, 4) Left Parenthesis 10 comma 4 Right Parenthesis
(−7, −1) Left Parenthesis negative 7 comma negative 1 Right Parenthesis
(−10, 4) Left Parenthesis negative 10 comma 4 Right Parenthesis
(4, 4)
(10, 4) has a distance of 3 from the point (-7, 4).
To find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, you can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case:
distance = sqrt((10 - (-7))^2 + (4 - 4)^2)
distance = sqrt((17)^2 + (0)^2)
distance = sqrt(289)
distance = 17
Since 17 is not equal to 3, this point is not 3 units away from (-7, 4).
Find the perimeter of rectangle EFGH , with vertices E(−3,9) , F(1,9) , G(1,−5) , and H(−3,−5) .
To find the perimeter of a rectangle with vertices given, you need to calculate the distance between each pair of consecutive vertices and then sum them up.
Let's calculate the distances between the vertices:
1. Distance between E and F:
distance_EF = sqrt((1 - (-3))^2 + (9 - 9)^2) = sqrt(4^2) = 4
2. Distance between F and G:
distance_FG = sqrt((1 - 1)^2 + (9 - (-5))^2) = sqrt(14^2) = 14
3. Distance between G and H:
distance_GH = sqrt((-3 - 1)^2 + (-5 - (-5))^2) = sqrt(4^2) = 4
4. Distance between H and E:
distance_HE = sqrt((-3 - (-3))^2 + (-5 - 9)^2) = sqrt(14^2) = 14
Now, sum up the distances to find the perimeter:
Perimeter = distance_EF + distance_FG + distance_GH + distance_HE
Perimeter = 4 + 14 + 4 + 14
Perimeter = 36
Therefore, the perimeter of rectangle EFGH is 36 units.