Use Coordinate Geometry to Solve Problems quick check

Answer 1

1. Find the midpoint of the line segment with endpoints at (-3, 4) and (5, -2).

Midpoint formula:
Midpoint = ( (x1 + x2)/2 , (y1 + y2)/2 )

Midpoint = ( (-3 + 5)/2 , (4 + (-2))/2 )
Midpoint = ( 2/2 , 2/2 )
Midpoint = (1, 1)

Therefore, the midpoint of the line segment is (1, 1).

2. Determine the distance between the points (1, 3) and (4, 7).

Distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Distance = √((4 - 1)^2 + (7 - 3)^2)
Distance = √(3^2 + 4^2)
Distance = √(9 + 16)
Distance = √25
Distance = 5

Therefore, the distance between the points (1, 3) and (4, 7) is 5 units.

Answer 2

Use the image to answer the question.

An illustration shows quadrant one of a coordinate plane with the x axis extending from 0 to 9 and the y axis extending from 0 to 9 in increments of 1. A quadrilateral upper A upper B upper C upper D is drawn on the coordinate plane. The coordinates of the rectangle are as follows: upper A left parenthesis 2 comma 5 right parenthesis, upper B left parenthesis 1 comma 3 right parenthesis, upper C left parenthesis 9 comma 3 right parenthesis, and upper D left parenthesis 9 comma 6 right parenthesis.

Find the length of line segment BC .

(1 point)
Responses

10 cm
10 cm

8 cm
8 cm

3 cm
3 cm

9 cm

Answer 3

To find the length of line segment BC, we use the distance formula:

BC = √((x2 - x1)^2 + (y2 - y1)^2)

Coordinates of B: (1, 3)
Coordinates of C: (9, 3)

BC = √((9 - 1)^2 + (3 - 3)^2)
BC = √(8^2)
BC = √64
BC = 8

Therefore, the length of line segment BC is 8 units.

The correct answer is:
8 cm