**Ex 7.4 Class 10 Maths Question 1.**

Determine the ratio, in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, -2) and B(3, 7).

**Ex 7.4 Class 10 Maths Question 2.**

Find a relation between x and y, if the points (x, y), (1, 2) and (7, 0) are collinear.

**Ex 7.4 Class 10 Maths Question 3.**

Find the centre of a circle passing through the points (6, -6), (3, -7) and (3, 3).

**Ex 7.4 Class 10 Maths Question 4.**

The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.

**Ex 7.4 Class 10 Maths Question 5.**

The class X students school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

(i) Taking A as origin, find the coordinates of the vertices of the triangle.

(ii) What will be the coordinates of the vertices of ∆PQR, if C is the origin?

Also, calculate the areas of the triangles in these cases. What do you observe?

**Ex 7.4 Class 10 Maths Question 6.**

The vertices of a VABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively. such that calculate the area of the ∆ADe and compare it with the area of ∆ABC.

**Ex 7.4 Class 10 Maths Question 7.**

Let A(4, 2), B(6,5) and C(1, 4) be the vertices of ∆ABC.

(i) The median from A meters BC at D. Find the coordinates of the point D.

(ii) Find the coordinates of the point P on the AD, such that AP: PD = 2: 1.

(iii) Find the coordinates of points Q and R on medians BE and CF respectively, such that BQ: QE = 2: 1 and CR: RF = 2: 1.

(iv) What do you observe?

[Note: The points which are common to all the three medians is called centroid and this point divides each median in the ratio 2: 1]

(v) If A(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}) are the vertices of ∆ABC, find the coordinates of the centroid of the triangles.

**Ex 7.4 Class 10 Maths Question 8.**

ABCD is a rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1), P, Q, R and S are the mid-points of Ab, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.