Post Test: Coordinate Geometry
What is the area of this triangle?
See image, or: A = 1/2(y2-y1)(x3-x1)
Based on the construction shown, what is the next step when bisecting line segment AB using string?
WRONG! The answer IS NOT "Set the string length between point A and where the arc crosses segment AB ."
Study this incomplete image of a geometric construction. This image may result from the construction of_________________________ The next step in this construction is to set the compass width to________________________________________
an angle congruent to a given angle; arc JK and draw an arc centered at L intersecting the existing arc through L
Mr. Williams drew the following image on the board and asked his students to write a sequence of steps explaining how to construct a line which passes through point C and is perpendicular to line AB. The work of two students, Elias and Greyson, is shown. Which student(s) successfully outlined a series of steps to complete the construction?
both Elias and Greyson
The given diagram shows a construction completed using a straightedge and a compass.
for copying angle ABC; 24
Jamal is using the distance formula to find the length, d, of the line segment. His work so far is shown. What is Jamal's next step? Jamal should find the_________ by ______________________________.
length of each leg; subtracting x coordinate and y coordinate
In the figure, lines HJ and KL are parallel. Match each angle relationship with the appropriate reason.
m∠HED = m∠FEJ----> Vertical angles theorem m∠LFG + m∠GFK = 180°----> linear pair m∠KFE = m∠FEJ----> Alternate internal angles theorem m∠LFG = m∠DEH----> Alternate external angles theorem m∠JEF + m∠LFE = 180°---> Same side interior angles m∠DEJ = m∠EFL----> Corresponding angles theorem
In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C?
(2,-1)
Segment AB, shown below, is divided into 5 equal parts. Point A is located at (-6,7), and point D is located at (-2,3). What are the coordinates of point F?
(2,-1)
In the figure, the ratio of the area of rectangle ABEF to the area of rectangle ACDF is .If the coordinates of point A are (0,6), the area of rectangle ABEF is square units, and the area of rectangle ACDF is square units.The perimeter of rectangle BCDE is units.
(MOSTLY correct 3/4) 2:3 ; 64.03 square units; (The area of ACDF is NOT 64.03 square units); 22.81 units
Line AB passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to Line AB?
-5x - 3y = 0.
The table and corresponding image show the proof of the relationship between the slopes of two parallel lines. What is the missing statement in step 2?
0 - a/c - 0 = - a/c
Line CD bisects AB― at point G. If AE = BE, which equation must be true?
AG = BG
In the figure below, u∥v. Prove: ∠3 and ∠5 are congruent.
Alternate exterior angle theorem; Transitive property of congruence
CD is perpendicular to AB and passes through point C (5,12).If the coordinates of A and B are (-10, -3) and (7, 14), respectively, the x- intercept of CD is:
CD is (17,0) The point (-2,19)
In the figure, line a and line b are parallel. Based on the figure, match each given angle with its congruent angles.
∠3,∠7,∠6 ---> angles congruent to ∠2 ∠3,∠7,∠2 ---> angles congruent to ∠6 ∠4,∠8,∠5 ---> angles congruent to ∠1 ∠3,∠6,∠2 ---> angles congruent to ∠7
The endpoints of GH are G(14,3) and H(10,-6). What is the midpoint of GH?
(12,-3/2)
The coordinates of point J are(-7,2) , and the midpoint of JK is at L(3,5). What are the coordinates of point K?
(13,8)
Two points located on JK⟷ are J(1,-4) and K(-2,8). What is the slope of JK⟷ ?
-4
Triangle ABC is defined by the points A(3,8), B(7,5), and C(2,3). Create an equation for a line passing through point A and perpendicular to BC.
y = -5/2x + 31/2
Type the correct answer in each box. If necessary, round your answers to the nearest hundredth. The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). The perimeter of ∆ABC is ________________ units, and its area is _________________ square units.
1/2 Correct , second part is right( The answer is NOT 34.22 units); 30 square units
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. On a number line, point F is at 4, and point G is at -2. Point H lies between point F and point G. If the ratio of FH to HG is 3 : 9, where does point H lie on the number line? Point H is at ___________ on the number line.
2.5
A group of college students built a self-guided rover and tested it on a plane surface. They programmed the vehicle to move along the path A-B-C-D-A represented on the coordinate plane. What distance will the rover cover if it completes one circuit?
40 meters
The endpoints of WX are W(5,-3) and X(-1,-9). What is the length of WX?
6√2.
