Question

SOLVE IT IT'S CHALLENGING !!!!!!!!

GRADE: 10
SUBJECT: MATHEMATICS
TOPIC: COORDINATE GEOMETRY

REVISION WORKSHEET
1. Write the formula used for finding out the distance between two points.
2. Write the formula for internal division.
3. Write the formula for area of a triangle.
4. Find the distance between the following pairs of points:
(i) (8, 4) , (4, 2) (ii) (-2, 1) , (-2, 5)
5. Determine whether the points (-3, 1) , (-2, 2) and (-1, 3) are collinear.
6. The end-points of a segment are plotted in the Cartesian plane. The end-points are
(0, -2) and (0, 5). Find the length of the line segment.
7. Determine whether the following pairs of points form a triangle:
(i) (4, 3) , (2, 1) , (5, 4) (ii) (4, -3) , (4, 3) , (0, 0)
8. Find the area of the ∆ XYZ by using the following coordinates:
X (4, -2), Y (9, -8), Z (10,-5)
9. Find the coordinates of the mid-point of seg PQ. The coordinates of P and Q are
(18, -6) and (8, -2) respectively.
10. Find the coordinates of the point M if it divides the line segment joining the points
P (-4, -8) and R (-6, -2) internally in the ratio 1:1.

Answer 1

Answer:

Ans1) Distance formula. Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points.

Ans 2) Internal Divisions with Section Formula. P = ( m x 2 + n x 1 m + n , m y 2 + n y 1 m + n ) .

Ans 3) To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.